Total Gift. Suppose you receive 10 on the firstday of the year, 12 on the 2nd day, 14 on

Determine whether the statement is true or false. A sequence is a function.

Determine whether the statement is true or false. An infinite geometric series with r = -1 has a limit.

Determine whether the statement is true or false. Permutations involve order and arrangements of objects. [

Determine whether the statement is true or false. The total number of subsets of a set with n elements is n2.

Determine whether the statement is true or false. Find the first 4 terms, a11, and a23: an = 1-12na n2 n4 + 1 b.

Determine whether the statement is true or false. Predict the general, or nth, term. Answers may vary. 2, -5, 10, -17, 26, c

Determine whether the statement is true or false. Find and evaluate: a 4 k=1 1-12k+13k 3k - 1 .

Determine whether the statement is true or false. Use a graphing calculator to construct a table of values and a graph for the first 10 terms of this sequence. a1 = 0.3, ak+1 = 5ak + 1

Determine whether the statement is true or false. Write sigma notation. Answers may vary. 0 + 3 + 8 + 15 + 24 + 35 + 48 [

Determine whether the statement is true or false. Find the 10th term of the arithmetic sequence 34 , 13 12, 17 12, c

Determine whether the statement is true or false. Find the 6th term of the arithmetic sequence a - b, a, a + b, c

Determine whether the statement is true or false. Find the sum of the first 18 terms of the arithmetic sequence 4, 7, 10, c

Determine whether the statement is true or false. Find the sum of the first 200 natural numbers

Determine whether the statement is true or false. The 1st term in an arithmetic sequence is 5, and the 17th term is 53. Find the 3rd term.

Determine whether the statement is true or false. The common difference in an arithmetic sequence is 3. The 10th term is 23. Find the first term. [

Determine whether the statement is true or false. For a geometric sequence, a1 = -2, r = 2, and an = -64. Find n and Sn.

Determine whether the statement is true or false. For a geometric sequence, r = 12 and S5 = 31 2 . Find a1 and a5. [

Find the sum of each infinite geometric series, if it exists. 25 + 27.5 + 30.25 + 33.275 +

Find the sum of each infinite geometric series, if it exists. 0.27 + 0.0027 + 0.000027 +

Find the sum of each infinite geometric series, if it exists. 12 - 16 + 1 18 - g

Find fraction notation for 2.43. [

Insert four arithmetic means between 5 and 9.

Bouncing Golfball. A golfball is dropped from a height of 30 ft to the pavement. It always rebounds three-fourths of the distance that it drops. How far (up and down) will the ball have traveled when it hits the pavement for the 6th time? [

The Amount of an Annuity. To create a college fund, a parent makes a sequence of 18 yearly deposits of $2000 each in a savings account on which interest is compounded annually at 2.8%. Find the amount of the annuity.

Total Gift. Suppose you receive 10 on the first day of the year, 12 on the 2nd day, 14 on the 3rd day, and so on. a) How much will you receive on the 365th day? [8.2] b) What is the sum of these 365 gifts?

The Economic Multiplier. Suppose the government is making a $24,000,000,000 expenditure for travel to Mars. If 73% of this amount is spent again, and so on, what is the total effect on the economy?

Use mathematical induction to prove each of the following. For every natural number n, 1 + 4 + 7 +g+ 13n - 22 = n13n - 12 2

Use mathematical induction to prove each of the following. For every natural number n, 1 + 3 + 32 + g+ 3n-1 = 3n - 1 2

Use mathematical induction to prove each of the following. For every natural number n 2, a1 - 1 2 b a1 - 1 3 bga1 - 1 n b = 1 n

Book Arrangements. In how many ways can 6 books be arranged on a shelf?

Flag Displays. If 9 different signal flags are available, how many different displays are possible using 4 flags in a row?

Prize Choices. The winner of a contest can choose any 8 of 15 prizes. How many different sets of prizes can be chosen?

FraternitySorority Names. The Greek alphabet contains 24 letters. How many fraternity or sorority names can be formed using 3 different letters?

Letter Arrangements. In how many distinguishable ways can the letters of the word TENNESSEE be arranged?

Floor Plans. A manufacturer of houses has 1 floor plan but achieves variety by having 3 different roofs, 4 different ways of attaching the garage, and 3 different types of entrances. Find the number of different houses that can be produced.

Code Symbols. How many code symbols can be formed using 5 out of 6 of the letters of G, H, I, J, K, L if the letters: a) cannot be repeated? [8.5] b) can be repeated? [8.5] c) cannot be repeated but must begin with K? [8.5] d) cannot be repeated but must end with IGH?

Determine the number of subsets of a set containing 8 members.

Expand. 1m + n27 1x - 2225

Expand. 1x - 2225

Expand. 1x2 - 3y24

Expand. aa + 1 a b 8

Expand. 11 + 5i26, where i2 = -1

Find the 4th term of 1a + x212.

Find the 12th term of 12a - b218. Do not multiply out the factorials.

Rolling Dice. What is the probability of getting a 10 on a roll of a pair of dice? on a roll of 1 die?

Drawing a Card. From a deck of 52 cards, 1 card is drawn at random. What is the probability that it is a club?

Drawing Three Cards. From a deck of 52 cards, 3 are drawn at random without replacement. What is the probability that 2 are aces and 1 is a king? [

Election Poll. Three people were running for mayor in an election campaign. A poll was conducted to see which candidate was favored. During the polling, 86 favored candidate A, 97 favored B, and 23 favored C. Assuming that the poll is a valid indicator of the election results, what is the probability that the election will be won by A? B? C?

Consumption of American Cheese. The table below lists the number of pounds of American cheese consumed per capita for selected years. a) Find a linear sequence function an = an + b that models the data. Let n represent the number of years since 1930. b) Use the sequence found in part(a) to estimate the number of pounds of American cheese consumed per capita in 2010.

Which of the following is the 25th term of the arithmetic sequence 12, 10, 8, 6, c? [8.2] A. -38 B. -36 C. 32 D. 60

What is the probability of getting a total of 4 on a roll of a pair of dice? [8.8] A. 1 12 B. 19 C. 16 D. 5 36

The graph of the sequence whose general term is an = n - 1 is which of the following?

Suppose that a1, a2, c, an and b1, b2, c, bn are geometric sequences. Prove that c1, c2, c, cn is a geometric sequence, where cn = anbn.

Suppose that a1, a2, c, an is an arithmetic sequence. Is b1, b2, c, bn an arithmetic sequence if: a) bn =  an  ? [8.2] b) bn = an + 8? [8.2] c) bn = 7an? [8.2] d) bn = 1 an ? [8.2] e) bn = log an? [8.2] f) bn = a3 n? [8.2

The zeros of this polynomial function form an arithmetic sequence. Find them. [8.2] f 1x2 = x4 - 4x3 - 4x2 + 16x

Write the first 3 terms of the infinite geometric series with r = -13 and S = 38 . [8.3]

Simplify: a 10 k=0 1-12ka 10 k b1log x210-k1log y2k.

Solve for n. a n 6 b = 3  a n - 1 5 b

Solve for n. n n - 1 b = 36

Solve for n. Solve for a: a 5 k=0 a 5 k b95-kak = 0.

How long is 15? Suppose you own 15 books and decide to make up all the possible arrangements of the books on a shelf. About how long, in years, would it take you if you were to make one arrangement per second? Write out the reasoning you used for this problem in the form of a paragraph.

Circular Arrangements. In how many ways can the numbers on a clock face be arranged? See if you can derive a formula for the number of distinct circular arrangements of n objects. Explain your reasoning.

Give an explanation that you might use with a fellow student to explain that a n k b = a n n - k b.

Explain why a combination lock should really be called a permutation lock.

Discuss the advantages and disadvantages of each method of finding a binomial expansion. Give examples of when you might use one method rather than the other.