 8.8.3.1: A sequence is called a ________ sequence when the ratios of consecu...
 8.8.6.1: The ________ ________ ________ states that when there are different...
 8.8.1.1: An ________ ________ is a function whose domain is the set of posit...
 8.8.4.1: The first step in proving a formula by ________ ________ is to show...
 8.8.7.1: An ________ is any happening for which the result is uncertain, and...
 8.8.2.1: A sequence is called an ________ sequence when the differences betw...
 8.8.5.1: The coefficients of a binomial expansion are called ________ ________.
 8.1: In Exercises 14, write the first five terms of the sequence. (Assum...
 8.8.3.2: The th term of a geometric sequence has the form ________.
 8.8.6.2: An ordering of elements is called a ________ of the elements.
 8.8.1.2: A sequence is a ________ sequence when the domain of the function c...
 8.8.4.2: To find the ________ differences of a sequence, subtract consecutiv...
 8.8.7.2: The set of all possible outcomes of an experiment is called the ___...
 8.8.2.2: The nth term of an arithmetic sequence has the form ________.
 8.8.5.2: To find binomial coefficients, you can use the ________ ________ or...
 8.2: In Exercises 14, write the first five terms of the sequence. (Assum...
 8.8.3.3: The sum of a finite geometric sequence with common ratio is given b...
 8.8.6.3: The number of permutations of elements taken at a time is given by ...
 8.8.1.3: If you are given one or more of the first few terms of a sequence, ...
 8.8.4.3: A sequence is an ________ sequence when the first differences are a...
 8.8.7.3: To determine the ________ of an event, you can use the formula wher...
 8.8.2.3: When you know the term of an arithmetic sequence and you know the c...
 8.8.5.3: The symbol used to denote a binomial coefficient is ________ or ___...
 8.3: In Exercises 14, write the first five terms of the sequence. (Assum...
 8.8.3.4: The sum of the terms of an infinite geometric sequence is called a ...
 8.8.6.4: The number of ________ ________ of objects is given by n!n1!n2!n3! ...
 8.8.1.4: If is a positive integer, then ________ is defined as n! 1 2 3 4 . ...
 8.8.4.4: If the ________ differences of a sequence are all the same nonzero ...
 8.8.7.4: If then is an ________ event, and if then is a ________ event.
 8.8.2.4: You can use the formula to find the sum of the first terms of an ar...
 8.8.5.4: When you write the coefficients for a binomial that is raised to a ...
 8.4: In Exercises 14, write the first five terms of the sequence. (Assum...
 8.8.3.5: In Exercises 512, determine whether the sequence is geometric. If s...
 8.8.6.5: When selecting subsets of a larger set in which order is not import...
 8.8.1.5: For the sum is called the ________ of summation, is the ________ li...
 8.8.4.5: In Exercises 510, find for the given Pk. Pk 5kk 1Pk
 8.8.7.5: If two events from the same sample space have no outcomes in common...
 8.8.2.5: In Exercises 512, determine whether the sequence is arithmetic. If ...
 8.8.5.5: In Exercises 514, find the binomial coefficient. 5C3
 8.5: In Exercises 58, write an expression for the apparent th term of th...
 8.8.3.6: In Exercises 512, determine whether the sequence is geometric. If s...
 8.8.6.6: The number of combinations of elements taken at a time is given by ...
 8.8.1.6: The sum of the terms of a finite or infinite sequence is called a _...
 8.8.4.6: In Exercises 510, find for the given Pk. Pk 12k 2Pk
 8.8.7.6: If the occurrence of one event has no effect on the occurrence of a...
 8.8.2.6: In Exercises 512, determine whether the sequence is arithmetic. If ...
 8.8.5.6: In Exercises 514, find the binomial coefficient. 8C6
 8.6: In Exercises 58, write an expression for the apparent th term of th...
 8.8.3.7: In Exercises 512, determine whether the sequence is geometric. If s...
 8.8.6.7: In Exercises 714, determine the number of ways a computer can rando...
 8.8.1.7: In Exercises 722, write the first five terms of the sequence. (Assu...
 8.8.4.7: In Exercises 510, find for the given Pk.P 2k 1k k 2k 326Pk 1
 8.8.7.7: The ________ of an event is the collection of all outcomes in the s...
 8.8.2.7: In Exercises 512, determine whether the sequence is arithmetic. If ...
 8.8.5.7: In Exercises 514, find the binomial coefficient. 12C0
 8.7: In Exercises 58, write an expression for the apparent th term of th...
 8.8.3.8: In Exercises 512, determine whether the sequence is geometric. If s...
 8.8.6.8: In Exercises 714, determine the number of ways a computer can rando...
 8.8.1.8: In Exercises 722, write the first five terms of the sequence. (Assu...
 8.8.4.8: In Exercises 510, find for the given Pk. Pk k3 P 2k 1k k
 8.8.7.8: Match the probability formula with the correct probability name. (a...
 8.8.2.8: In Exercises 512, determine whether the sequence is arithmetic. If ...
 8.8.5.8: In Exercises 514, find the binomial coefficient. 20C20
 8.8: In Exercises 58, write an expression for the apparent th term of th...
 8.8.3.9: In Exercises 512, determine whether the sequence is geometric. If s...
 8.8.6.9: In Exercises 714, determine the number of ways a computer can rando...
 8.8.1.9: In Exercises 722, write the first five terms of the sequence. (Assu...
 8.8.4.9: In Exercises 510, find for the given Pk. Pk 3k 2k 3Pk k
 8.8.7.9: In Exercises 914, find the sample space for the experiment. You tos...
 8.8.2.9: In Exercises 512, determine whether the sequence is arithmetic. If ...
 8.8.5.9: In Exercises 514, find the binomial coefficient. 20C15
 8.9: In Exercises 912, simplify the factorial expression. 9!
 8.8.3.10: In Exercises 512, determine whether the sequence is geometric. If s...
 8.8.6.10: In Exercises 714, determine the number of ways a computer can rando...
 8.8.1.10: In Exercises 722, write the first five terms of the sequence. (Assu...
 8.8.4.10: In Exercises 510, find for the given Pk. Pk k22k 12 Pk
 8.8.7.10: In Exercises 914, find the sample space for the experiment. You tos...
 8.8.2.10: In Exercises 512, determine whether the sequence is arithmetic. If ...
 8.8.5.10: In Exercises 514, find the binomial coefficient. 12C5
 8.10: In Exercises 912, simplify the factorial expression. 4! 0!
 8.8.3.11: In Exercises 512, determine whether the sequence is geometric. If s...
 8.8.6.11: In Exercises 714, determine the number of ways a computer can rando...
 8.8.1.11: In Exercises 722, write the first five terms of the sequence. (Assu...
 8.8.4.11: In Exercises 1124, use mathematical induction to prove the formula ...
 8.8.7.11: In Exercises 914, find the sample space for the experiment. A taste...
 8.8.2.11: In Exercises 512, determine whether the sequence is arithmetic. If ...
 8.8.5.11: In Exercises 514, find the binomial coefficient. 104
 8.11: In Exercises 912, simplify the factorial expression. 3! 5!6!
 8.8.3.12: In Exercises 512, determine whether the sequence is geometric. If s...
 8.8.6.12: In Exercises 714, determine the number of ways a computer can rando...
 8.8.1.12: In Exercises 722, write the first five terms of the sequence. (Assu...
 8.8.4.12: In Exercises 1124, use mathematical induction to prove the formula ...
 8.8.7.12: In Exercises 914, find the sample space for the experiment. You sel...
 8.8.2.12: In Exercises 512, determine whether the sequence is arithmetic. If ...
 8.8.5.12: In Exercises 514, find the binomial coefficient. 106
 8.12: In Exercises 912, simplify the factorial expression. 7! 6!6! 8!
 8.8.3.13: In Exercises 1322, write the first five terms of the geometric sequ...
 8.8.6.13: In Exercises 714, determine the number of ways a computer can rando...
 8.8.1.13: In Exercises 722, write the first five terms of the sequence. (Assu...
 8.8.4.13: In Exercises 1124, use mathematical induction to prove the formula ...
 8.8.7.13: In Exercises 914, find the sample space for the experiment. Two cou...
 8.8.2.13: In Exercises 1320, write the first five terms of the sequence. Dete...
 8.8.5.13: In Exercises 514, find the binomial coefficient. 10098
 8.13: In Exercises 13 and 14, find the sum. 4j 16j 2
 8.8.3.14: In Exercises 1322, write the first five terms of the geometric sequ...
 8.8.6.14: In Exercises 714, determine the number of ways a computer can rando...
 8.8.1.14: In Exercises 722, write the first five terms of the sequence. (Assu...
 8.8.4.14: In Exercises 1124, use mathematical induction to prove the formula ...
 8.8.7.14: In Exercises 914, find the sample space for the experiment. A sales...
 8.8.2.14: In Exercises 1320, write the first five terms of the sequence. Dete...
 8.8.5.14: In Exercises 514, find the binomial coefficient. 1002
 8.14: In Exercises 13 and 14, find the sum. 10k12k3
 8.8.3.15: In Exercises 1322, write the first five terms of the geometric sequ...
 8.8.6.15: Entertainment Systems A customer can choose one of three amplifiers...
 8.8.1.15: In Exercises 722, write the first five terms of the sequence. (Assu...
 8.8.4.15: In Exercises 1124, use mathematical induction to prove the formula ...
 8.8.7.15: In Exercises 1520, find the probability for the experiment of tossi...
 8.8.2.15: In Exercises 1320, write the first five terms of the sequence. Dete...
 8.8.5.15: In Exercises 1518, evaluate using Pascals Triangle. 65
 8.15: In Exercises 15 and 16, use sigma notation to write the sum. 121122...
 8.8.3.16: In Exercises 1322, write the first five terms of the geometric sequ...
 8.8.6.16: Job Applicants A small college needs two additional faculty members...
 8.8.1.16: In Exercises 722, write the first five terms of the sequence. (Assu...
 8.8.4.16: In Exercises 1124, use mathematical induction to prove the formula ...
 8.8.7.16: In Exercises 1520, find the probability for the experiment of tossi...
 8.8.2.16: In Exercises 1320, write the first five terms of the sequence. Dete...
 8.8.5.16: In Exercises 1518, evaluate using Pascals Triangle. 52
 8.16: In Exercises 15 and 16, use sigma notation to write the sum. 122334...
 8.8.3.17: In Exercises 1322, write the first five terms of the geometric sequ...
 8.8.6.17: Course Schedule A college student is preparing a course schedule fo...
 8.8.1.17: In Exercises 722, write the first five terms of the sequence. (Assu...
 8.8.4.17: In Exercises 1124, use mathematical induction to prove the formula ...
 8.8.7.17: In Exercises 1520, find the probability for the experiment of tossi...
 8.8.2.17: In Exercises 1320, write the first five terms of the sequence. Dete...
 8.8.5.17: In Exercises 1518, evaluate using Pascals Triangle. 7C4
 8.17: In Exercises 17 and 18, find the sum of the infinite series. i1410i
 8.8.3.18: In Exercises 1322, write the first five terms of the geometric sequ...
 8.8.6.18: Aircraft Boarding Eight people are boarding an aircraft. Two have t...
 8.8.1.18: In Exercises 722, write the first five terms of the sequence. (Assu...
 8.8.4.18: In Exercises 1124, use mathematical induction to prove the formula ...
 8.8.7.18: In Exercises 1520, find the probability for the experiment of tossi...
 8.8.2.18: In Exercises 1320, write the first five terms of the sequence. Dete...
 8.8.5.18: In Exercises 1518, evaluate using Pascals Triangle. 10C2
 8.18: In Exercises 17 and 18, find the sum of the infinite series. k121100k
 8.8.3.19: In Exercises 1322, write the first five terms of the geometric sequ...
 8.8.6.19: TrueFalse Exam In how many ways can you answer a sixquestion true...
 8.8.1.19: In Exercises 722, write the first five terms of the sequence. (Assu...
 8.8.4.19: In Exercises 1124, use mathematical induction to prove the formula ...
 8.8.7.19: In Exercises 1520, find the probability for the experiment of tossi...
 8.8.2.19: In Exercises 1320, write the first five terms of the sequence. Dete...
 8.8.5.19: In Exercises 1940, use the Binomial Theorem to expand and simplify ...
 8.19: Compound Interest An investor deposits $10,000 in an account that e...
 8.8.3.20: In Exercises 1322, write the first five terms of the geometric sequ...
 8.8.6.20: TrueFalse Exam In how many ways can you answer a 12question true...
 8.8.1.20: In Exercises 722, write the first five terms of the sequence. (Assu...
 8.8.4.20: In Exercises 1124, use mathematical induction to prove the formula ...
 8.8.7.20: In Exercises 1520, find the probability for the experiment of tossi...
 8.8.2.20: In Exercises 1320, write the first five terms of the sequence. Dete...
 8.8.5.20: In Exercises 1940, use the Binomial Theorem to expand and simplify ...
 8.20: Lottery Ticket Sales The total sales (in billions of dollars) of lo...
 8.8.3.21: In Exercises 1322, write the first five terms of the geometric sequ...
 8.8.6.21: License Plate Numbers In the state of Pennsylvania, each standard a...
 8.8.1.21: In Exercises 722, write the first five terms of the sequence. (Assu...
 8.8.4.21: In Exercises 1124, use mathematical induction to prove the formula ...
 8.8.7.21: In Exercises 2124, find the probability for the experiment of drawi...
 8.8.2.21: In Exercises 2130, find a formula for for the arithmetic sequence. ...
 8.8.5.21: In Exercises 1940, use the Binomial Theorem to expand and simplify ...
 8.21: In Exercises 2124, determine whether the sequence is arithmetic. If...
 8.8.3.22: In Exercises 1322, write the first five terms of the geometric sequ...
 8.8.6.22: License Plate Numbers In a certain state, each automobile license p...
 8.8.1.22: In Exercises 722, write the first five terms of the sequence. (Assu...
 8.8.4.22: In Exercises 1124, use mathematical induction to prove the formula ...
 8.8.7.22: In Exercises 2124, find the probability for the experiment of drawi...
 8.8.2.22: In Exercises 2130, find a formula for for the arithmetic sequence. ...
 8.8.5.22: In Exercises 1940, use the Binomial Theorem to expand and simplify ...
 8.22: In Exercises 2124, determine whether the sequence is arithmetic. If...
 8.8.3.23: In Exercises 2328, write the first five terms of the geometric sequ...
 8.8.6.23: ThreeDigit Numbers How many threedigit numbers can you form under...
 8.8.1.23: In Exercises 2326, find the indicated term of the sequence. a nn 1n...
 8.8.4.23: In Exercises 1124, use mathematical induction to prove the formula ...
 8.8.7.23: In Exercises 2124, find the probability for the experiment of drawi...
 8.8.2.23: In Exercises 2130, find a formula for for the arithmetic sequence. ...
 8.8.5.23: In Exercises 1940, use the Binomial Theorem to expand and simplify ...
 8.23: In Exercises 2124, determine whether the sequence is arithmetic. If...
 8.8.3.24: In Exercises 2328, write the first five terms of the geometric sequ...
 8.8.6.24: FourDigit Numbers How many fourdigit numbers can you form under e...
 8.8.1.24: In Exercises 2326, find the indicated term of the sequence. an 1n1 ...
 8.8.4.24: In Exercises 1124, use mathematical induction to prove the formula ...
 8.8.7.24: In Exercises 2124, find the probability for the experiment of drawi...
 8.8.2.24: In Exercises 2130, find a formula for for the arithmetic sequence. ...
 8.8.5.24: In Exercises 1940, use the Binomial Theorem to expand and simplify ...
 8.24: In Exercises 2124, determine whether the sequence is arithmetic. If...
 8.8.3.25: In Exercises 2328, write the first five terms of the geometric sequ...
 8.8.6.25: Combination Lock A combination lock will open when you select the r...
 8.8.1.25: In Exercises 2326, find the indicated term of the sequence. an 4n2n...
 8.8.4.25: In Exercises 2530, use mathematical induction to prove the inequali...
 8.8.7.25: In Exercises 2530, find the probability for the experiment of tossi...
 8.8.2.25: In Exercises 2130, find a formula for for the arithmetic sequence. ...
 8.8.5.25: In Exercises 1940, use the Binomial Theorem to expand and simplify ...
 8.25: In Exercises 2528, find a formula for for the arithmetic sequence a...
 8.8.3.26: In Exercises 2328, write the first five terms of the geometric sequ...
 8.8.6.26: Combination Lock A combination lock will open when you select the r...
 8.8.1.26: In Exercises 2326, find the indicated term of the sequence. an 4n2 ...
 8.8.4.26: In Exercises 2530, use mathematical induction to prove the inequali...
 8.8.7.26: In Exercises 2530, find the probability for the experiment of tossi...
 8.8.2.26: In Exercises 2130, find a formula for for the arithmetic sequence. ...
 8.8.5.26: In Exercises 1940, use the Binomial Theorem to expand and simplify ...
 8.26: In Exercises 2528, find a formula for for the arithmetic sequence a...
 8.8.3.27: In Exercises 2328, write the first five terms of the geometric sequ...
 8.8.6.27: Concert Seats Four couples have reserved seats in one row for a con...
 8.8.1.27: In Exercises 2732, use a graphing utility to graph the first 10 ter...
 8.8.4.27: In Exercises 2530, use mathematical induction to prove the inequali...
 8.8.7.27: In Exercises 2530, find the probability for the experiment of tossi...
 8.8.2.27: In Exercises 2130, find a formula for for the arithmetic sequence. ...
 8.8.5.27: In Exercises 1940, use the Binomial Theorem to expand and simplify ...
 8.27: In Exercises 2528, find a formula for for the arithmetic sequence a...
 8.8.3.28: In Exercises 2328, write the first five terms of the geometric sequ...
 8.8.6.28: Single File In how many orders can four girls and four boys walk th...
 8.8.1.28: In Exercises 2732, use a graphing utility to graph the first 10 ter...
 8.8.4.28: In Exercises 2530, use mathematical induction to prove the inequali...
 8.8.7.28: In Exercises 2530, find the probability for the experiment of tossi...
 8.8.2.28: In Exercises 2130, find a formula for for the arithmetic sequence. ...
 8.8.5.28: In Exercises 1940, use the Binomial Theorem to expand and simplify ...
 8.28: In Exercises 2528, find a formula for for the arithmetic sequence a...
 8.8.3.29: In Exercises 2938, write an expression for the th term of the geome...
 8.8.6.29: Posing for a Photograph In how many ways can five children posing f...
 8.8.1.29: In Exercises 2732, use a graphing utility to graph the first 10 ter...
 8.8.4.29: In Exercises 2530, use mathematical induction to prove the inequali...
 8.8.7.29: In Exercises 2530, find the probability for the experiment of tossi...
 8.8.2.29: In Exercises 2130, find a formula for for the arithmetic sequence. ...
 8.8.5.29: In Exercises 1940, use the Binomial Theorem to expand and simplify ...
 8.29: In Exercises 29 and 30, write the first five terms of the arithmeti...
 8.8.3.30: In Exercises 2938, write an expression for the th term of the geome...
 8.8.6.30: Riding in a Car In how many ways can six people sit in a sixpassen...
 8.8.1.30: In Exercises 2732, use a graphing utility to graph the first 10 ter...
 8.8.4.30: In Exercises 2530, use mathematical induction to prove the inequali...
 8.8.7.30: In Exercises 2530, find the probability for the experiment of tossi...
 8.8.2.30: In Exercises 2130, find a formula for for the arithmetic sequence. ...
 8.8.5.30: In Exercises 1940, use the Binomial Theorem to expand and simplify ...
 8.30: In Exercises 29 and 30, write the first five terms of the arithmeti...
 8.8.3.31: In Exercises 2938, write an expression for the th term of the geome...
 8.8.6.31: In Exercises 3134, evaluate nPr 4P4
 8.8.1.31: In Exercises 2732, use a graphing utility to graph the first 10 ter...
 8.8.4.31: In Exercises 3140, use mathematical induction to prove the property...
 8.8.7.31: In Exercises 3134, find the probability for the experiment of drawi...
 8.8.2.31: In Exercises 3138, write the first five terms of the arithmetic seq...
 8.8.5.31: In Exercises 1940, use the Binomial Theorem to expand and simplify ...
 8.31: Sum of a Finite Arithmetic Sequence Find the sum of the first 100 p...
 8.8.3.32: In Exercises 2938, write an expression for the th term of the geome...
 8.8.6.32: In Exercises 3134, evaluate nPr 8P3
 8.8.1.32: In Exercises 2732, use a graphing utility to graph the first 10 ter...
 8.8.4.32: In Exercises 3140, use mathematical induction to prove the property...
 8.8.7.32: In Exercises 3134, find the probability for the experiment of drawi...
 8.8.2.32: In Exercises 3138, write the first five terms of the arithmetic seq...
 8.8.5.32: In Exercises 1940, use the Binomial Theorem to expand and simplify ...
 8.32: Sum of a Finite Arithmetic Sequence Find the sum of the integers fr...
 8.8.3.33: In Exercises 2938, write an expression for the th term of the geome...
 8.8.6.33: In Exercises 3134, evaluate nPr 20P2
 8.8.1.33: In Exercises 3336, match the sequence with the graph of its first 1...
 8.8.4.33: In Exercises 3140, use mathematical induction to prove the property...
 8.8.7.33: In Exercises 3134, find the probability for the experiment of drawi...
 8.8.2.33: In Exercises 3138, write the first five terms of the arithmetic seq...
 8.8.5.33: In Exercises 1940, use the Binomial Theorem to expand and simplify ...
 8.33: In Exercises 3336, find the partial sum. 20 3j10j12j 3a1 3,
 8.8.3.34: In Exercises 2938, write an expression for the th term of the geome...
 8.8.6.34: In Exercises 3134, evaluate nPr 5P4
 8.8.1.34: In Exercises 3336, match the sequence with the graph of its first 1...
 8.8.4.34: In Exercises 3140, use mathematical induction to prove the property...
 8.8.7.34: In Exercises 3134, find the probability for the experiment of drawi...
 8.8.2.34: In Exercises 3138, write the first five terms of the arithmetic seq...
 8.8.5.34: In Exercises 1940, use the Binomial Theorem to expand and simplify ...
 8.34: In Exercises 3336, find the partial sum. 8j120 3
 8.8.3.35: In Exercises 2938, write an expression for the th term of the geome...
 8.8.6.35: In Exercises 3538, evaluate using a graphing utility. 20P5
 8.8.1.35: In Exercises 3336, match the sequence with the graph of its first 1...
 8.8.4.35: In Exercises 3140, use mathematical induction to prove the property...
 8.8.7.35: Graphical Reasoning In 2011, there were approximately 13.75 million...
 8.8.2.35: In Exercises 3138, write the first five terms of the arithmetic seq...
 8.8.5.35: In Exercises 1940, use the Binomial Theorem to expand and simplify ...
 8.35: In Exercises 3336, find the partial sum. 11k123k 4
 8.8.3.36: In Exercises 2938, write an expression for the th term of the geome...
 8.8.6.36: In Exercises 3538, evaluate using a graphing utility. 100P5
 8.8.1.36: In Exercises 3336, match the sequence with the graph of its first 1...
 8.8.4.36: In Exercises 3140, use mathematical induction to prove the property...
 8.8.7.36: Data Analysis An independent polling organization interviews one hu...
 8.8.2.36: In Exercises 3138, write the first five terms of the arithmetic seq...
 8.8.5.36: In Exercises 1940, use the Binomial Theorem to expand and simplify ...
 8.36: In Exercises 3336, find the partial sum. 25k13k 14
 8.8.3.37: In Exercises 2938, write an expression for the th term of the geome...
 8.8.6.37: In Exercises 3538, evaluate using a graphing utility. 100P3
 8.8.1.37: In Exercises 3748, write an expression for the apparent th term of ...
 8.8.4.37: In Exercises 3140, use mathematical induction to prove the property...
 8.8.7.37: Education In a high school graduating class of 128 students, 52 are...
 8.8.2.37: In Exercises 3138, write the first five terms of the arithmetic seq...
 8.8.5.37: In Exercises 1940, use the Binomial Theorem to expand and simplify ...
 8.37: Job Offer The starting salary for a job is $43,800 with a guarantee...
 8.8.3.38: In Exercises 2938, write an expression for the th term of the geome...
 8.8.6.38: In Exercises 3538, evaluate using a graphing utility. 10P8
 8.8.1.38: In Exercises 3748, write an expression for the apparent th term of ...
 8.8.4.38: In Exercises 3140, use mathematical induction to prove the property...
 8.8.7.38: Alumni Association A college sends a survey to members of the class...
 8.8.2.38: In Exercises 3138, write the first five terms of the arithmetic seq...
 8.8.5.38: In Exercises 1940, use the Binomial Theorem to expand and simplify ...
 8.38: Baling Hay In the first two trips baling hay around a large field, ...
 8.39: In Exercises 3942, determine whether the sequence is geometric. If ...
 8.8.3.39: In Exercises 3946, find the indicated term of the geometric sequenc...
 8.8.6.39: A patient with endstage kidney disease has nine family members who...
 8.8.1.39: In Exercises 3748, write an expression for the apparent th term of ...
 8.8.4.39: In Exercises 3140, use mathematical induction to prove the property...
 8.8.7.39: Winning an Election Three people are running for president of a cla...
 8.8.2.39: In Exercises 3942, write the first five terms of the arithmetic seq...
 8.8.5.39: In Exercises 1940, use the Binomial Theorem to expand and simplify ...
 8.40: In Exercises 3942, determine whether the sequence is geometric. If ...
 8.8.3.40: In Exercises 3946, find the indicated term of the geometric sequenc...
 8.8.6.40: Choosing Officers From a pool of 12 candidates, the offices of pres...
 8.8.1.40: In Exercises 3748, write an expression for the apparent th term of ...
 8.8.4.40: In Exercises 3140, use mathematical induction to prove the property...
 8.8.7.40: Payroll Error The employees of a company work in six departments: 3...
 8.8.2.40: In Exercises 3942, write the first five terms of the arithmetic seq...
 8.8.5.40: In Exercises 1940, use the Binomial Theorem to expand and simplify ...
 8.41: In Exercises 3942, determine whether the sequence is geometric. If ...
 8.8.3.41: In Exercises 3946, find the indicated term of the geometric sequenc...
 8.8.6.41: Batting Order A baseball coach is creating a nineplayer batting or...
 8.8.1.41: In Exercises 3748, write an expression for the apparent th term of ...
 8.8.4.41: In Exercises 4144, use mathematical induction to find a formula for...
 8.8.7.41: In Exercises 4148, the sample spaces are large and you should use t...
 8.8.2.41: In Exercises 3942, write the first five terms of the arithmetic seq...
 8.8.5.41: In Exercises 41 44, expand the binomial by using Pascals Triangle t...
 8.42: In Exercises 3942, determine whether the sequence is geometric. If ...
 8.8.3.42: In Exercises 3946, find the indicated term of the geometric sequenc...
 8.8.6.42: Athletics Eight sprinters have qualified for the finals in the 100...
 8.8.1.42: In Exercises 3748, write an expression for the apparent th term of ...
 8.8.4.42: In Exercises 4144, use mathematical induction to find a formula for...
 8.8.7.42: In Exercises 4148, the sample spaces are large and you should use t...
 8.8.2.42: In Exercises 3942, write the first five terms of the arithmetic seq...
 8.8.5.42: In Exercises 41 44, expand the binomial by using Pascals Triangle t...
 8.43: In Exercises 4346, write the first five terms of the geometric sequ...
 8.8.3.43: In Exercises 3946, find the indicated term of the geometric sequenc...
 8.8.6.43: In Exercises 4346, find the number of distinguishable permutations ...
 8.8.1.43: In Exercises 3748, write an expression for the apparent th term of ...
 8.8.4.43: In Exercises 4144, use mathematical induction to find a formula for...
 8.8.7.43: In Exercises 4148, the sample spaces are large and you should use t...
 8.8.2.43: In Exercises 4346, the first two terms of the arithmetic sequence a...
 8.8.5.43: In Exercises 41 44, expand the binomial by using Pascals Triangle t...
 8.44: In Exercises 4346, write the first five terms of the geometric sequ...
 8.8.3.44: In Exercises 3946, find the indicated term of the geometric sequenc...
 8.8.6.44: In Exercises 4346, find the number of distinguishable permutations ...
 8.8.1.44: In Exercises 3748, write an expression for the apparent th term of ...
 8.8.4.44: In Exercises 4144, use mathematical induction to find a formula for...
 8.8.7.44: In Exercises 4148, the sample spaces are large and you should use t...
 8.8.2.44: In Exercises 4346, the first two terms of the arithmetic sequence a...
 8.8.5.44: In Exercises 41 44, expand the binomial by using Pascals Triangle t...
 8.8.5.45: In Exercises 4552, find the specified th term in the expansion of t...
 8.45: In Exercises 4346, write the first five terms of the geometric sequ...
 8.8.3.45: In Exercises 3946, find the indicated term of the geometric sequenc...
 8.8.6.45: In Exercises 4346, find the number of distinguishable permutations ...
 8.8.1.45: In Exercises 3748, write an expression for the apparent th term of ...
 8.8.4.45: In Exercises 4554, find the sum using the formulas for the sums of ...
 8.8.7.45: In Exercises 4148, the sample spaces are large and you should use t...
 8.8.2.45: In Exercises 4346, the first two terms of the arithmetic sequence a...
 8.8.5.46: In Exercises 4552, find the specified th term in the expansion of t...
 8.46: In Exercises 4346, write the first five terms of the geometric sequ...
 8.8.3.46: In Exercises 3946, find the indicated term of the geometric sequenc...
 8.8.6.46: In Exercises 4346, find the number of distinguishable permutations ...
 8.8.1.46: In Exercises 3748, write an expression for the apparent th term of ...
 8.8.4.46: In Exercises 4554, find the sum using the formulas for the sums of ...
 8.8.7.46: In Exercises 4148, the sample spaces are large and you should use t...
 8.8.2.46: In Exercises 4346, the first two terms of the arithmetic sequence a...
 8.8.5.47: In Exercises 4552, find the specified th term in the expansion of t...
 8.47: In Exercises 4750, write an expression for the th term of the geome...
 8.8.3.47: In Exercises 4750, match the geometric sequence with its graph. [Th...
 8.8.6.47: . Writing Permutations Write all permutations of the letters A, B, ...
 8.8.1.47: In Exercises 3748, write an expression for the apparent th term of ...
 8.8.4.47: In Exercises 4554, find the sum using the formulas for the sums of ...
 8.8.7.47: In Exercises 4148, the sample spaces are large and you should use t...
 8.8.2.47: In Exercises 4752, find the sum of the finite arithmetic sequence. ...
 8.8.5.48: In Exercises 4552, find the specified th term in the expansion of t...
 8.48: In Exercises 4750, write an expression for the th term of the geome...
 8.8.3.48: In Exercises 4750, match the geometric sequence with its graph. [Th...
 8.8.6.48: Writing Permutations Write all permutations of the letters A, B, C,...
 8.8.1.48: In Exercises 3748, write an expression for the apparent th term of ...
 8.8.4.48: In Exercises 4554, find the sum using the formulas for the sums of ...
 8.8.7.48: In Exercises 4148, the sample spaces are large and you should use t...
 8.8.2.48: In Exercises 4752, find the sum of the finite arithmetic sequence. ...
 8.8.5.49: In Exercises 4552, find the specified th term in the expansion of t...
 8.49: In Exercises 4750, write an expression for the th term of the geome...
 8.8.3.49: In Exercises 4750, match the geometric sequence with its graph. [Th...
 8.8.6.49: In Exercises 4952, evaluate using the formula from this section. 5C2
 8.8.1.49: In Exercises 4952, write the first five terms of the sequence defin...
 8.8.4.49: In Exercises 4554, find the sum using the formulas for the sums of ...
 8.8.7.49: Random Number Generator A random number generator on a computer sel...
 8.8.2.49: In Exercises 4752, find the sum of the finite arithmetic sequence. ...
 8.8.5.50: In Exercises 4552, find the specified th term in the expansion of t...
 8.50: In Exercises 4750, write an expression for the th term of the geome...
 8.8.3.50: In Exercises 4750, match the geometric sequence with its graph. [Th...
 8.8.6.50: In Exercises 4952, evaluate using the formula from this section. 6C3
 8.8.1.50: In Exercises 4952, write the first five terms of the sequence defin...
 8.8.4.50: In Exercises 4554, find the sum using the formulas for the sums of ...
 8.8.7.50: Flexible Work Hours In a survey, people were asked whether they wou...
 8.8.2.50: In Exercises 4752, find the sum of the finite arithmetic sequence. ...
 8.8.5.51: In Exercises 4552, find the specified th term in the expansion of t...
 8.51: In Exercises 5156, find the sum of the finite geometric sequence. 7...
 8.8.3.51: In Exercises 5154, use a graphing utility to graph the first 10 ter...
 8.8.6.51: In Exercises 4952, evaluate using the formula from this section. 6C3
 8.8.1.51: In Exercises 4952, write the first five terms of the sequence defin...
 8.8.4.51: In Exercises 4554, find the sum using the formulas for the sums of ...
 8.8.7.51: In Exercises 5154, you are given the probability that an event will...
 8.8.2.51: In Exercises 4752, find the sum of the finite arithmetic sequence. ...
 8.8.5.52: In Exercises 4552, find the specified th term in the expansion of t...
 8.52: In Exercises 5156, find the sum of the finite geometric sequence. 5...
 8.8.3.52: In Exercises 5154, use a graphing utility to graph the first 10 ter...
 8.8.6.52: In Exercises 4952, evaluate using the formula from this section. 25C0
 8.8.1.52: In Exercises 4952, write the first five terms of the sequence defin...
 8.8.4.52: In Exercises 4554, find the sum using the formulas for the sums of ...
 8.8.7.52: In Exercises 5154, you are given the probability that an event will...
 8.8.2.52: In Exercises 4752, find the sum of the finite arithmetic sequence. ...
 8.8.5.53: In Exercises 5360, find the coefficient of the term in the expansio...
 8.53: In Exercises 5156, find the sum of the finite geometric sequence. 4...
 8.8.3.53: In Exercises 5154, use a graphing utility to graph the first 10 ter...
 8.8.6.53: In Exercises 5356, evaluate using a graphing utility. 20C4
 8.8.1.53: In Exercises 5356, write the first five terms of the sequence defin...
 8.8.4.53: In Exercises 4554, find the sum using the formulas for the sums of ...
 8.8.7.53: In Exercises 5154, you are given the probability that an event will...
 8.8.2.53: In Exercises 5358, find the indicated th partial sum of the arithme...
 8.8.5.54: In Exercises 5360, find the coefficient of the term in the expansio...
 8.54: In Exercises 5156, find the sum of the finite geometric sequence. 6...
 8.8.3.54: In Exercises 5154, use a graphing utility to graph the first 10 ter...
 8.8.6.54: In Exercises 5356, evaluate using a graphing utility. 10C7
 8.8.1.54: In Exercises 5356, write the first five terms of the sequence defin...
 8.8.4.54: In Exercises 4554, find the sum using the formulas for the sums of ...
 8.8.7.54: In Exercises 5154, you are given the probability that an event will...
 8.8.2.54: In Exercises 5358, find the indicated th partial sum of the arithme...
 8.8.5.55: In Exercises 5360, find the coefficient of the term in the expansio...
 8.55: In Exercises 5156, find the sum of the finite geometric sequence. 5...
 8.8.3.55: In Exercises 5568, find the sum of the finite geometric sequence. n...
 8.8.6.55: In Exercises 5356, evaluate using a graphing utility. 42C5
 8.8.1.55: In Exercises 5356, write the first five terms of the sequence defin...
 8.8.4.55: In Exercises 5560, decide whether the sequence can be represented p...
 8.8.7.55: In Exercises 5558, you are given the probability that an event will...
 8.8.2.55: In Exercises 5358, find the indicated th partial sum of the arithme...
 8.8.5.56: In Exercises 5360, find the coefficient of the term in the expansio...
 8.56: In Exercises 5156, find the sum of the finite geometric sequence. 4...
 8.8.3.56: In Exercises 5568, find the sum of the finite geometric sequence. 1...
 8.8.6.56: In Exercises 5356, evaluate using a graphing utility. 50C6
 8.8.1.56: In Exercises 5356, write the first five terms of the sequence defin...
 8.8.4.56: In Exercises 5560, decide whether the sequence can be represented p...
 8.8.7.56: In Exercises 5558, you are given the probability that an event will...
 8.8.2.56: In Exercises 5358, find the indicated th partial sum of the arithme...
 8.8.5.57: In Exercises 5360, find the coefficient of the term in the expansio...
 8.57: In Exercises 57 and 58, use a graphing utility to find the sum of t...
 8.8.3.57: In Exercises 5568, find the sum of the finite geometric sequence. 6...
 8.8.6.57: Writing Combinations Write all combinations of two letters that you...
 8.8.1.57: In Exercises 57 and 58, use the Fibonacci sequence. (See Example 5....
 8.8.4.57: In Exercises 5560, decide whether the sequence can be represented p...
 8.8.7.57: In Exercises 5558, you are given the probability that an event will...
 8.8.2.57: In Exercises 5358, find the indicated th partial sum of the arithme...
 8.8.2.58: In Exercises 5358, find the indicated th partial sum of the arithme...
 8.8.5.58: In Exercises 5360, find the coefficient of the term in the expansio...
 8.58: In Exercises 57 and 58, use a graphing utility to find the sum of t...
 8.8.3.58: In Exercises 5568, find the sum of the finite geometric sequence. 8...
 8.8.6.58: Forming an Experimental Group In order to conduct an experiment, re...
 8.8.1.58: In Exercises 57 and 58, use the Fibonacci sequence. (See Example 5....
 8.8.4.58: In Exercises 5560, decide whether the sequence can be represented p...
 8.8.7.58: In Exercises 5558, you are given the probability that an event will...
 8.8.2.59: In Exercises 5964, find the partial sum. 50n1n
 8.8.5.59: In Exercises 5360, find the coefficient of the term in the expansio...
 8.59: In Exercises 5962, find the sum of the infinite geometric series. i...
 8.8.3.59: In Exercises 5568, find the sum of the finite geometric sequence. 7...
 8.8.6.59: Jury Selection In how many different ways can a jury of 12 people b...
 8.8.1.59: In Exercises 5962, write the first five terms of the sequence. (Ass...
 8.8.4.59: In Exercises 5560, decide whether the sequence can be represented p...
 8.8.7.59: A space vehicle has an independent backup system for one of its com...
 8.8.2.60: In Exercises 5964, find the partial sum. 100n517n
 8.8.5.60: In Exercises 5360, find the coefficient of the term in the expansio...
 8.60: In Exercises 5962, find the sum of the infinite geometric series. i...
 8.8.3.60: In Exercises 5568, find the sum of the finite geometric sequence. 1...
 8.8.6.60: Committee Members A U.S. Senate Committee has 14 members. Assuming ...
 8.8.1.60: In Exercises 5962, write the first five terms of the sequence. (Ass...
 8.8.4.60: In Exercises 5560, decide whether the sequence can be represented p...
 8.8.7.60: Backup Vehicle A fire company keeps two rescue vehicles. Because of...
 8.8.2.61: In Exercises 5964, find the partial sum. 30n11n 10n1n
 8.8.5.61: In Exercises 6166, use the Binomial Theorem to expand and simplify ...
 8.61: In Exercises 5962, find the sum of the infinite geometric series. k...
 8.8.3.61: In Exercises 5568, find the sum of the finite geometric sequence. 2...
 8.8.6.61: Lottery Choices In the Massachusetts Mass Cash game, a player rando...
 8.8.1.61: In Exercises 5962, write the first five terms of the sequence. (Ass...
 8.8.4.61: In Exercises 6168, write the first six terms of the sequence beginn...
 8.8.7.61: Roulette American roulette is a game in which a wheel turns on a sp...
 8.8.2.62: In Exercises 5964, find the partial sum. 100n51n 50n1n30
 8.8.5.62: In Exercises 6166, use the Binomial Theorem to expand and simplify ...
 8.62: In Exercises 5962, find the sum of the infinite geometric series. k...
 8.8.3.62: In Exercises 5568, find the sum of the finite geometric sequence. 4...
 8.8.6.62: Lottery Choices In the Louisiana Lotto game, a player randomly choo...
 8.8.1.62: In Exercises 5962, write the first five terms of the sequence. (Ass...
 8.8.4.62: In Exercises 6168, write the first six terms of the sequence beginn...
 8.8.7.62: Boy or a Girl? Assume that the probability of the birth of a child ...
 8.8.2.63: In Exercises 5964, find the partial sum. 500n1n 8
 8.8.5.63: In Exercises 6166, use the Binomial Theorem to expand and simplify ...
 8.63: Depreciation A paper manufacturer buys a machine for $120,000. Duri...
 8.8.3.63: In Exercises 5568, find the sum of the finite geometric sequence. 2...
 8.8.6.63: Defective Units A shipment of 25 television sets contains three def...
 8.8.1.63: In Exercises 6366, simplify the factorial expression. 4!6!
 8.8.4.63: In Exercises 6168, write the first six terms of the sequence beginn...
 8.8.7.63: Geometry You and a friend agree to meet at your favorite fastfood ...
 8.8.2.64: In Exercises 5964, find the partial sum. 250n11000 n50
 8.8.5.64: In Exercises 6166, use the Binomial Theorem to expand and simplify ...
 8.64: Annuity An investor deposits $800 in an account on the first day of...
 8.8.3.64: In Exercises 5568, find the sum of the finite geometric sequence. 6...
 8.8.6.64: Interpersonal Relationships The complexity of interpersonal relatio...
 8.8.1.64: In Exercises 6366, simplify the factorial expression. 12!4! 8!
 8.8.4.64: In Exercises 6168, write the first six terms of the sequence beginn...
 8.8.7.64: Estimating You drop a coin of diameter onto a paper that contains a...
 8.8.2.65: In Exercises 6568, match the arithmetic sequence with its graph. [T...
 8.8.5.65: In Exercises 6166, use the Binomial Theorem to expand and simplify ...
 8.65: In Exercises 6568, use mathematical induction to prove the formula ...
 8.8.3.65: In Exercises 5568, find the sum of the finite geometric sequence. 4...
 8.8.6.65: Poker Hand You are dealt five cards from a standard deck of 52 play...
 8.8.1.65: In Exercises 6366, simplify the factorial expression. n 1!n!1
 8.8.4.65: In Exercises 6168, write the first six terms of the sequence beginn...
 8.8.7.65: In Exercises 65 and 66, determine whether the statement is true or ...
 8.8.2.66: In Exercises 6568, match the arithmetic sequence with its graph. [T...
 8.8.5.66: In Exercises 6166, use the Binomial Theorem to expand and simplify ...
 8.66: In Exercises 6568, use mathematical induction to prove the formula ...
 8.8.3.66: In Exercises 5568, find the sum of the finite geometric sequence. 5...
 8.8.6.66: Job Applicants An employer interviews 12 people for four openings a...
 8.8.1.66: In Exercises 6366, simplify the factorial expression. 2n 1!2n 1!n
 8.8.4.66: In Exercises 6168, write the first six terms of the sequence beginn...
 8.8.7.66: In Exercises 65 and 66, determine whether the statement is true or ...
 8.8.2.67: In Exercises 6568, match the arithmetic sequence with its graph. [T...
 8.8.5.67: In Exercises 6772, simplify the difference quotient, using the Bino...
 8.67: In Exercises 6568, use mathematical induction to prove the formula ...
 8.8.3.67: In Exercises 5568, find the sum of the finite geometric sequence. 1...
 8.8.6.67: Forming a Committee A local college is forming a sixmember researc...
 8.8.1.67: In Exercises 6774, find the sum. 2 35i12i 12n
 8.8.4.67: In Exercises 6168, write the first six terms of the sequence beginn...
 8.8.7.67: Pattern Recognition Consider a group of people. (a) Explain why the...
 8.8.2.68: In Exercises 6568, match the arithmetic sequence with its graph. [T...
 8.8.5.68: In Exercises 6772, simplify the difference quotient, using the Bino...
 8.68: In Exercises 6568, use mathematical induction to prove the formula ...
 8.8.3.68: In Exercises 5568, find the sum of the finite geometric sequence.10...
 8.8.6.68: Law Enforcement A police department uses computer imaging to create...
 8.8.1.68: In Exercises 6774, find the sum. 5j31j 2 3
 8.8.4.68: In Exercises 6168, write the first six terms of the sequence beginn...
 8.8.7.68: HOW DO YOU SEE IT? The circle graphs show the percents of undergrad...
 8.8.2.69: In Exercises 6972, use a graphing utility to graph the first 10 ter...
 8.8.5.69: In Exercises 6772, simplify the difference quotient, using the Bino...
 8.69: In Exercises 6972, use mathematical induction to find a formula for...
 8.8.3.69: In Exercises 6972, use summation notation to write the sum. 10 30 9...
 8.8.6.69: In Exercises 6972, find the number of diagonals of the polygon. (A ...
 8.8.1.69: In Exercises 6774, find the sum. 4k110
 8.8.4.69: In Exercises 6974, find a quadratic model for the sequence with the...
 8.8.2.70: In Exercises 6972, use a graphing utility to graph the first 10 ter...
 8.8.5.70: In Exercises 6772, simplify the difference quotient, using the Bino...
 8.70: In Exercises 6972, use mathematical induction to find a formula for...
 8.8.3.70: In Exercises 6972, use summation notation to write the sum. 15 3 35...
 8.8.6.70: In Exercises 6972, find the number of diagonals of the polygon. (A ...
 8.8.1.70: In Exercises 6774, find the sum. 4i0i 2
 8.8.4.70: In Exercises 6974, find a quadratic model for the sequence with the...
 8.8.2.71: In Exercises 6972, use a graphing utility to graph the first 10 ter...
 8.8.5.71: In Exercises 6772, simplify the difference quotient, using the Bino...
 8.71: In Exercises 6972, use mathematical induction to find a formula for...
 8.8.3.71: In Exercises 6972, use summation notation to write the sum. 0.1 0.4...
 8.8.6.71: In Exercises 6972, find the number of diagonals of the polygon. (A ...
 8.8.1.71: In Exercises 6774, find the sum. 5k2k 12k 34
 8.8.4.71: In Exercises 6974, find a quadratic model for the sequence with the...
 8.8.2.72: In Exercises 6972, use a graphing utility to graph the first 10 ter...
 8.8.5.72: In Exercises 6772, simplify the difference quotient, using the Bino...
 8.72: In Exercises 6972, use mathematical induction to find a formula for...
 8.8.3.72: In Exercises 6972, use summation notation to write the sum. 32 24 1...
 8.8.6.72: In Exercises 6972, find the number of diagonals of the polygon. (A ...
 8.8.1.72: In Exercises 6774, find the sum. 4i1i 12 i 135k2
 8.8.4.72: In Exercises 6974, find a quadratic model for the sequence with the...
 8.8.2.73: In Exercises 7376, use a graphing utility to find the partial sum. ...
 8.8.5.73: In Exercises 7378, use the Binomial Theorem to expand the complex n...
 8.73: In Exercises 73 and 74, find the sum using the formulas for the sum...
 8.8.3.73: In Exercises 7380, find the sum of the infinite geometric series. n...
 8.8.6.73: Geometry Three points that are not collinear determine three lines....
 8.8.1.73: In Exercises 6774, find the sum. 4i12i
 8.8.4.73: In Exercises 6974, find a quadratic model for the sequence with the...
 8.8.2.74: In Exercises 7376, use a graphing utility to find the partial sum. ...
 8.8.5.74: In Exercises 7378, use the Binomial Theorem to expand the complex n...
 8.74: In Exercises 73 and 74, find the sum using the formulas for the sum...
 8.8.3.74: In Exercises 7380, find the sum of the infinite geometric series. n...
 8.8.6.74: Lottery Powerball is a lottery game that is operated by the MultiS...
 8.8.1.74: In Exercises 6774, find the sum. 4j02j
 8.8.4.74: In Exercises 6974, find a quadratic model for the sequence with the...
 8.8.2.75: In Exercises 7376, use a graphing utility to find the partial sum. ...
 8.8.5.75: In Exercises 7378, use the Binomial Theorem to expand the complex n...
 8.75: In Exercises 75 and 76, write the first five terms of the sequence ...
 8.8.3.75: In Exercises 7380, find the sum of the infinite geometric series.n0...
 8.8.6.75: In Exercises 7582, solve for n 4 n1P2 n2P3 5
 8.8.1.75: In Exercises 7578, use a graphing utility to find the sum. 5n012n 1
 8.8.4.75: The table shows the numbers (in thousands) of Alaskan residents fro...
 8.8.2.76: In Exercises 7376, use a graphing utility to find the partial sum. ...
 8.8.5.76: In Exercises 7378, use the Binomial Theorem to expand the complex n...
 8.76: In Exercises 75 and 76, write the first five terms of the sequence ...
 8.8.3.76: In Exercises 7380, find the sum of the infinite geometric series. n...
 8.8.6.76: In Exercises 7582, solve for n 5 n1P1 nP2
 8.8.1.76: In Exercises 7578, use a graphing utility to find the sum. 4k01kk 15
 8.8.4.76: HOW DO YOU SEE IT? Find a formula for the sum of the angles (in deg...
 8.8.2.77: Seating Capacity Determine the seating capacity of an auditorium wi...
 8.8.5.77: In Exercises 7378, use the Binomial Theorem to expand the complex n...
 8.77: In Exercises 77 and 78, find the binomial coefficient. 6C4
 8.8.3.77: In Exercises 7380, find the sum of the infinite geometric series. 8...
 8.8.6.77: In Exercises 7582, solve for n n1P3 n2P3 6 n2P1 4 nP24
 8.8.1.77: In Exercises 7578, use a graphing utility to find the sum.4k01kk!
 8.8.4.77: In Exercises 77 and 78, determine whether the statement is true or ...
 8.8.2.78: Brick Pattern A triangular brick wall is made by cutting some brick...
 8.8.5.78: In Exercises 7378, use the Binomial Theorem to expand the complex n...
 8.78: In Exercises 77 and 78, find the binomial coefficient. 12C3
 8.8.3.78: In Exercises 7380, find the sum of the infinite geometric series. 9...
 8.8.6.78: In Exercises 7582, solve for n n2P3 6 n2P1 4
 8.8.1.78: In Exercises 7578, use a graphing utility to find the sum. 25n014 n
 8.8.4.78: In Exercises 77 and 78, determine whether the statement is true or ...
 8.8.2.79: In Exercises 79 and 80, consider a job offer with the given startin...
 8.8.5.79: In Exercises 7982, use the Binomial Theorem to approximate the quan...
 8.79: In Exercises 79 and 80, evaluate using Pascals Triangle. 72
 8.8.3.79: In Exercises 7380, find the sum of the infinite geometric series. 9...
 8.8.6.79: In Exercises 7582, solve for n 4 nP3 n2P4
 8.8.1.79: In Exercises 7988, use sigma notation to write the sum. 131132133. ...
 8.8.2.80: In Exercises 79 and 80, consider a job offer with the given startin...
 8.8.5.80: In Exercises 7982, use the Binomial Theorem to approximate the quan...
 8.80: In Exercises 79 and 80, evaluate using Pascals Triangle. 104
 8.8.3.80: In Exercises 7380, find the sum of the infinite geometric series. 1...
 8.8.6.80: In Exercises 7582, solve for n nP5 18 n2P4 1
 8.8.1.80: In Exercises 7988, use sigma notation to write the sum. 51 151 251 ...
 8.8.2.81: An object with negligible air resistance is dropped from the top of...
 8.8.5.81: In Exercises 7982, use the Binomial Theorem to approximate the quan...
 8.81: In Exercises 8184, use the Binomial Theorem to expand and simplify ...
 8.8.3.81: In Exercises 81 and 82, find the rational number representation of ...
 8.8.6.81: In Exercises 7582, solve for n nP4 nP6 12 n1P5 10 n1P3nP
 8.8.1.81: In Exercises 7988, use sigma notation to write the sum. 21832283. ....
 8.8.2.82: Prize Money A county fair is holding a baked goods competition in w...
 8.8.5.82: In Exercises 7982, use the Binomial Theorem to approximate the quan...
 8.82: In Exercises 8184, use the Binomial Theorem to expand and simplify ...
 8.8.3.82: In Exercises 81 and 82, find the rational number representation of ...
 8.8.6.82: In Exercises 7582, solve for n nP6 12 n1P5 1
 8.8.1.82: In Exercises 7988, use sigma notation to write the sum. 1 1621 262....
 8.8.2.83: Total Sales An entrepreneur sells $15,000 worth of sports memorabil...
 8.8.5.83: In Exercises 83 and 84, use a graphing utility to graph and in the ...
 8.83: In Exercises 8184, use the Binomial Theorem to expand and simplify ...
 8.8.3.83: In Exercises 83 and 84, use a graphing utility to graph the functio...
 8.8.6.83: In Exercises 83 and 84, determine whether the statement is true or ...
 8.8.1.83: In Exercises 7988, use sigma notation to write the sum. 3 9 27 81 2...
 8.8.2.84: Borrowing Money You borrow $5000 from your parents to purchase a us...
 8.8.5.84: In Exercises 83 and 84, use a graphing utility to graph and in the ...
 8.84: In Exercises 8184, use the Binomial Theorem to expand and simplify ...
 8.8.3.84: In Exercises 83 and 84, use a graphing utility to graph the functio...
 8.8.6.84: In Exercises 83 and 84, determine whether the statement is true or ...
 8.8.1.84: In Exercises 7988, use sigma notation to write the sum. 1 12 14 18 ...
 8.8.2.85: Data Analysis: Sales The table shows the sales (in billions of doll...
 8.8.5.85: In Exercises 8588, consider independent trials of an experiment in ...
 8.85: Numbers in a Hat You place slips of paper numbered 1 through 14 in ...
 8.8.3.85: Depreciation A tool and die company buys a machine for $175,000 and...
 8.8.6.85: Think About It Without calculating the numbers, determine which of ...
 8.8.1.85: In Exercises 7988, use sigma notation to write the sum. 12 122132 1...
 8.8.2.86: Writing Explain how to use the first two terms of an arithmetic seq...
 8.8.5.86: In Exercises 8588, consider independent trials of an experiment in ...
 8.86: Shopping A customer in an electronics store can choose one of six s...
 8.8.3.86: The table shows the midyear populations of China (in millions) fro...
 8.8.6.86: HOW DO YOU SEE IT? Without calculating, determine whether the value...
 8.8.1.86: In Exercises 7988, use sigma notation to write the sum. 1 312 413 5...
 8.8.2.87: In Exercises 87 and 88, determine whether the statement is true or ...
 8.8.5.87: In Exercises 8588, consider independent trials of an experiment in ...
 8.87: Telephone Numbers All of the land line telephone numbers in a small...
 8.8.3.87: Annuity An investor deposits dollars on the first day of each month...
 8.8.6.87: n Exercises 8790, prove the identity. nPn 1 nPn
 8.8.1.87: In Exercises 7988, use sigma notation to write the sum. 14 38 716 1...
 8.8.2.88: In Exercises 87 and 88, determine whether the statement is true or ...
 8.8.5.88: In Exercises 8588, consider independent trials of an experiment in ...
 8.88: Course Schedule A college student is preparing a course schedule fo...
 8.8.3.88: Annuity An investor deposits $100 on the first day of each month in...
 8.8.6.88: n Exercises 8790, prove the identity. Cn nC0
 8.8.1.88: In Exercises 7988, use sigma notation to write the sum. 12 24 68 24...
 8.8.2.89: In Exercises 89 and 90, find the first 10 terms of the sequence. a ...
 8.8.5.89: Finding a Pattern Describe the pattern formed by the sums of the nu...
 8.89: Genetics A geneticist is using gel electrophoresis to analyze five ...
 8.8.3.89: In Exercises 89 and 90, use the following information. A state gove...
 8.8.6.89: n Exercises 8790, prove the identity. nCn 1 nC1
 8.8.1.89: In Exercises 8992, find the indicated partial sum of the series. i1...
 8.8.2.90: In Exercises 89 and 90, find the first 10 terms of the sequence. a1...
 8.8.5.90: Finding a Pattern Use each of the encircled groups of numbers in th...
 8.90: Race There are 10 bicyclists entered in a race. In how many differe...
 8.8.3.90: In Exercises 89 and 90, use the following information. A state gove...
 8.8.6.90: n Exercises 8790, prove the identity. nCr nPr
 8.8.1.90: In Exercises 8992, find the indicated partial sum of the series. i1...
 8.8.2.91: Comparing Graphs of a Sequence and a Line (a) Graph the first 10 te...
 8.8.5.91: Child Support The amounts (in billions of dollars) of child support...
 8.91: Jury Selection A group of potential jurors has been narrowed down t...
 8.8.3.91: Geometry The sides of a square are 27 inches in length. New squares...
 8.8.6.91: Think About It Can your graphing utility evaluate If not, then expl...
 8.8.1.91: In Exercises 8992, find the indicated partial sum of the series. n1...
 8.8.2.92: HOW DO YOU SEE IT? A steel ball with negligible air resistance is d...
 8.8.5.92: The table shows the average prices (in cents per kilowatt hour) of ...
 8.92: Menu Choices A local sub shop offers five different breads, four di...
 8.8.3.92: Distance A ball is dropped from a height of 6 feet and begins bounc...
 8.8.1.92: In Exercises 8992, find the indicated partial sum of the series. n1...
 8.8.2.93: Pattern Recognition (a) Compute the following sums of consecutive p...
 8.8.5.93: In Exercises 93 and 94, determine whether the statement is true or ...
 8.93: Apparel A man has five pairs of socks, of which no two pairs are th...
 8.8.3.93: Salary An investment firm has a job opening with a salary of $45,00...
 8.8.1.93: In Exercises 9396, find the sum of the infinite series. i1610i
 8.8.5.94: In Exercises 93 and 94, determine whether the statement is true or ...
 8.94: Bookshelf Order A child returns a fivevolume set of books to a boo...
 8.8.3.94: HOW DO YOU SEE IT? Use the figures shown below. (i) (ii) (a) Withou...
 8.8.1.94: In Exercises 9396, find the sum of the infinite series. k1110
 8.8.5.95: Writing In your own words, explain how to form the rows of Pascals ...
 8.95: Students by Class At a university, 31% of the students are freshmen...
 8.8.3.95: In Exercises 95 and 96, determine whether the statement is true or ...
 8.8.1.95: In Exercises 9396, find the sum of the infinite series. k17110k
 8.8.5.96: Forming Rows of Pascals Triangle Formrows 810 of Pascals Triangle.
 8.96: Data Analysis Interviewers asked a sample of college students, facu...
 8.8.3.96: In Exercises 95 and 96, determine whether the statement is true or ...
 8.8.1.96: In Exercises 9396, find the sum of the infinite series. i1210 i
 8.8.5.97: Graphical Reasoning Which two functions have identical graphs, and ...
 8.97: Tossing a Die You toss a sixsided die four times. What is the prob...
 8.8.3.97: In Exercises 95 and 96, determine whether the statement is true or ...
 8.8.1.97: Compound Interest An investor deposits $10,000 in an account that e...
 8.8.5.98: HOW DO YOU SEE IT? The expansions of and are as follows. (a) Explai...
 8.98: Tossing a Die You toss a sixsided die six times. What is the proba...
 8.8.3.98: In Exercises 95 and 96, determine whether the statement is true or ...
 8.8.1.98: The numbers (in thousands) of AIDS cases reported from 2003 through...
 8.8.5.99: In Exercises 99102, prove the property for all integers and where n...
 8.99: Drawing a Card You randomly draw a card from a standard deck of 52 ...
 8.8.1.99: In Exercises 99 and 100, determine whether the statement is true or...
 8.8.5.100: In Exercises 99102, prove the property for all integers and where n...
 8.100: Tossing a Coin Find the probability of obtaining at least one tail ...
 8.8.1.100: In Exercises 99 and 100, determine whether the statement is true or...
 8.8.5.101: In Exercises 99102, prove the property for all integers and where n...
 8.101: In Exercises 101104, determine whether the statement is true or fal...
 8.8.1.101: In Exercises 101103, use the following definition of the arithmetic...
 8.8.5.102: In Exercises 99102, prove the property for all integers and where n...
 8.102: In Exercises 101104, determine whether the statement is true or fal...
 8.8.1.102: In Exercises 101103, use the following definition of the arithmetic...
 8.8.5.103: Binomial Coefficients and Pascals Triangle Complete the table and d...
 8.103: In Exercises 101104, determine whether the statement is true or fal...
 8.8.1.103: In Exercises 101103, use the following definition of the arithmetic...
 8.104: In Exercises 101104, determine whether the statement is true or fal...
 8.8.1.104: HOW DO YOU SEE IT? The graph represents the first 10 terms of a seq...
 8.105: Think About It An infinite sequence is a function. What is the doma...
 8.8.1.105: In Exercises 105 and 106, find the first five terms of the sequence...
 8.106: Think About It How do the two sequences differ? an 1nn an 1n1nan
 8.8.1.106: In Exercises 105 and 106, find the first five terms of the sequence...
 8.107: Writing Explain what is meant by a recursion formula.
 8.8.1.107: Cube A cube is made up of 27 unit cubes (a unit cube has a length, ...
 8.108: Writing Write a brief paragraph explaining how to identify the grap...
Solutions for Chapter 8: Sequences, Series, and Probability
Full solutions for College Algebra  9th Edition
ISBN: 9781133963028
Solutions for Chapter 8: Sequences, Series, and Probability
Get Full SolutionsCollege Algebra was written by and is associated to the ISBN: 9781133963028. Since 746 problems in chapter 8: Sequences, Series, and Probability have been answered, more than 36779 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 8: Sequences, Series, and Probability includes 746 full stepbystep solutions. This textbook survival guide was created for the textbook: College Algebra, edition: 9.

Back substitution.
Upper triangular systems are solved in reverse order Xn to Xl.

Big formula for n by n determinants.
Det(A) is a sum of n! terms. For each term: Multiply one entry from each row and column of A: rows in order 1, ... , nand column order given by a permutation P. Each of the n! P 's has a + or  sign.

Companion matrix.
Put CI, ... ,Cn in row n and put n  1 ones just above the main diagonal. Then det(A  AI) = ±(CI + c2A + C3A 2 + .•. + cnA nl  An).

Dot product = Inner product x T y = XI Y 1 + ... + Xn Yn.
Complex dot product is x T Y . Perpendicular vectors have x T y = O. (AB)ij = (row i of A)T(column j of B).

Exponential eAt = I + At + (At)2 12! + ...
has derivative AeAt; eAt u(O) solves u' = Au.

GaussJordan method.
Invert A by row operations on [A I] to reach [I AI].

Hermitian matrix A H = AT = A.
Complex analog a j i = aU of a symmetric matrix.

Multiplication Ax
= Xl (column 1) + ... + xn(column n) = combination of columns.

Normal equation AT Ax = ATb.
Gives the least squares solution to Ax = b if A has full rank n (independent columns). The equation says that (columns of A)·(b  Ax) = o.

Orthonormal vectors q 1 , ... , q n·
Dot products are q T q j = 0 if i =1= j and q T q i = 1. The matrix Q with these orthonormal columns has Q T Q = I. If m = n then Q T = Q 1 and q 1 ' ... , q n is an orthonormal basis for Rn : every v = L (v T q j )q j •

Particular solution x p.
Any solution to Ax = b; often x p has free variables = o.

Projection matrix P onto subspace S.
Projection p = P b is the closest point to b in S, error e = b  Pb is perpendicularto S. p 2 = P = pT, eigenvalues are 1 or 0, eigenvectors are in S or S...L. If columns of A = basis for S then P = A (AT A) 1 AT.

Rank r (A)
= number of pivots = dimension of column space = dimension of row space.

Simplex method for linear programming.
The minimum cost vector x * is found by moving from comer to lower cost comer along the edges of the feasible set (where the constraints Ax = b and x > 0 are satisfied). Minimum cost at a comer!

Standard basis for Rn.
Columns of n by n identity matrix (written i ,j ,k in R3).

Subspace S of V.
Any vector space inside V, including V and Z = {zero vector only}.

Triangle inequality II u + v II < II u II + II v II.
For matrix norms II A + B II < II A II + II B II·

Unitary matrix UH = U T = UI.
Orthonormal columns (complex analog of Q).

Vandermonde matrix V.
V c = b gives coefficients of p(x) = Co + ... + Cn_IXn 1 with P(Xi) = bi. Vij = (Xi)jI and det V = product of (Xk  Xi) for k > i.

Wavelets Wjk(t).
Stretch and shift the time axis to create Wjk(t) = woo(2j t  k).