 8.47: In Exercises 4750, determine whether the sequence isgeometric. If s...
 8.48: In Exercises 4750, determine whether the sequence isgeometric. If s...
 8.49: In Exercises 4750, determine whether the sequence isgeometric. If s...
 8.50: In Exercises 4750, determine whether the sequence isgeometric. If s...
 8.51: In Exercises 5154, write the first five terms of the geometricseque...
 8.52: In Exercises 5154, write the first five terms of the geometricseque...
 8.53: In Exercises 5154, write the first five terms of the geometricseque...
 8.54: In Exercises 5154, write the first five terms of the geometricseque...
 8.55: In Exercises 5558, write an expression for the th term ofthe geomet...
 8.56: In Exercises 5558, write an expression for the th term ofthe geomet...
 8.57: In Exercises 5558, write an expression for the th term ofthe geomet...
 8.58: In Exercises 5558, write an expression for the th term ofthe geomet...
 8.59: In Exercises 5964, find the sum of the finite geometricsequence.
 8.60: In Exercises 5964, find the sum of the finite geometricsequence.
 8.61: In Exercises 5964, find the sum of the finite geometricsequence.
 8.62: In Exercises 5964, find the sum of the finite geometricsequence.
 8.63: In Exercises 5964, find the sum of the finite geometricsequence.
 8.64: In Exercises 5964, find the sum of the finite geometricsequence.
 8.65: In Exercises 65 and 66, use a graphing utility to find the sumof th...
 8.66: In Exercises 65 and 66, use a graphing utility to find the sumof th...
 8.67: In Exercises 6770, find the sum of the infinite geometricseries.
 8.68: In Exercises 6770, find the sum of the infinite geometricseries.
 8.69: In Exercises 6770, find the sum of the infinite geometricseries.
 8.70: In Exercises 6770, find the sum of the infinite geometricseries.
 8.71: DEPRECIATION A paper manufacturer buys amachine for $120,000. Durin...
 8.72: ANNUITY You deposit $800 in an account at thebeginning of each mont...
 8.73: In Exercises 7376, use mathematical induction toprove the formula f...
 8.74: In Exercises 7376, use mathematical induction toprove the formula f...
 8.75: In Exercises 7376, use mathematical induction toprove the formula f...
 8.76: In Exercises 7376, use mathematical induction toprove the formula f...
 8.77: In Exercises 77 80, find a formula for the sum of the firstterms of...
 8.78: In Exercises 77 80, find a formula for the sum of the firstterms of...
 8.79: In Exercises 77 80, find a formula for the sum of the firstterms of...
 8.80: In Exercises 77 80, find a formula for the sum of the firstterms of...
 8.81: In Exercises 81 and 82, find the sum using the formulas forthe sums...
 8.82: In Exercises 81 and 82, find the sum using the formulas forthe sums...
 8.83: In Exercises 8386, write the first five terms of the sequencebeginn...
 8.84: In Exercises 8386, write the first five terms of the sequencebeginn...
 8.85: In Exercises 8386, write the first five terms of the sequencebeginn...
 8.86: In Exercises 8386, write the first five terms of the sequencebeginn...
 8.87: In Exercises 87 and 88, use the Binomial Theorem tocalculate the bi...
 8.88: In Exercises 87 and 88, use the Binomial Theorem tocalculate the bi...
 8.89: In Exercises 89 and 90, use Pascals Triangle to calculate thebinomi...
 8.90: In Exercises 89 and 90, use Pascals Triangle to calculate thebinomi...
 8.91: In Exercises 9196, use the Binomial Theorem to expand andsimplify t...
 8.92: In Exercises 9196, use the Binomial Theorem to expand andsimplify t...
 8.93: In Exercises 9196, use the Binomial Theorem to expand andsimplify t...
 8.94: In Exercises 9196, use the Binomial Theorem to expand andsimplify t...
 8.95: In Exercises 9196, use the Binomial Theorem to expand andsimplify t...
 8.96: In Exercises 9196, use the Binomial Theorem to expand andsimplify t...
 8.97: NUMBERS IN A HAT Slips of paper numbered 1through 14 are placed in ...
 8.98: SHOPPING A customer in an electronics store can chooseone of six sp...
 8.99: TELEPHONE NUMBERS The same threedigit prefixis used for all of the...
 8.100: COURSE SCHEDULE A college student is preparinga course schedule for...
 8.101: RACE There are 10 bicyclists entered in a race. In howmany differen...
 8.102: JURY SELECTION A group of potential jurors hasbeen narrowed down to...
 8.103: APPAREL You have eight different suits to choosefrom to take on a t...
 8.104: MENU CHOICES A local sub shop offers five differentbreads, four dif...
 8.105: APPAREL A man has five pairs of socks, of whichno two pairs are the...
 8.106: BOOKSHELF ORDER A child returns a fivevolumeset of books to a book...
 8.107: STUDENTS BY CLASS At a particular university, thenumber of students...
 8.108: DATA ANALYSIS A sample of college students, faculty,and administrat...
 8.109: TOSSING A DIE A sixsided die is tossed four times.What is the prob...
 8.110: TOSSING A DIE A sixsided die is tossed six times.What is the proba...
 8.111: DRAWING A CARD You randomly select a cardfrom a 52card deck. What ...
 8.112: TOSSING A COIN Find the probability of obtainingat least one tail w...
 8.113: TRUE OR FALSE? In Exercises 113116, determinewhether the statement ...
 8.114: TRUE OR FALSE? In Exercises 113116, determinewhether the statement ...
 8.115: TRUE OR FALSE? In Exercises 113116, determinewhether the statement ...
 8.116: TRUE OR FALSE? In Exercises 113116, determinewhether the statement ...
 8.117: THINK ABOUT IT An infinite sequence is a function.What is the domai...
 8.118: THINK ABOUT IT How do the two sequences differ?
 8.119: WRITING Explain what is meant by a recursion formula.
 8.120: WRITING Write a brief paragraph explaining how toidentify the graph...
 8.20: The percents (by age group) of the total amounts spent on three typ...
 8.21: In Exercises 21 and 22, use Cramers Rule to solve the system of equ...
 8.22: In Exercises 21 and 22, use Cramers Rule to solve the system of equ...
 8.23: Find the area of the triangle shown in the figure.
 8.24: Write the first five terms of the sequence (Assume that beginswith 1.)
 8.25: Write an expression for the th term of the sequence.
 8.26: Find the sum of the first 16 terms of the arithmetic sequence 6, 18...
 8.27: The sixth term of an arithmetic sequence is 20.6, and the ninth ter...
 8.28: Write the first five terms of the sequence (Assume that beginswith 1.)
 8.29: Find the sum: i01.3 110i1.
 8.30: Use mathematical induction to prove the formula 3 7 11 15 . . . 4n ...
 8.31: Use the Binomial Theorem to expand and simplify w 94.
 8.32: In Exercises 3235, evaluate the expression.
 8.33: In Exercises 3235, evaluate the expression.
 8.34: In Exercises 3235, evaluate the expression.
 8.35: In Exercises 3235, evaluate the expression.
 8.36: In Exercises 36 and 37, find the number of distinguishable permutat...
 8.37: In Exercises 36 and 37, find the number of distinguishable permutat...
 8.38: A personnel manager at a department store has 10 applicants to fill...
 8.39: On a game show, the digits 3, 4, and 5 must be arranged in the prop...
 8.1: Let and consider the sequence given byUse a graphing utility to com...
 8.2: Consider the sequence(a) Use a graphing utility to graph the first ...
 8.3: Consider the sequence(a) Use a graphing utility to graph the first ...
 8.4: The following operations are performed on each term of anarithmetic...
 8.5: The following sequence of perfect squares is notarithmetic.1, 4, 9,...
 8.6: Can the Greek hero Achilles, running at 20 feet persecond, ever cat...
 8.7: Recall that a fractal is a geometric figure that consists ofa patte...
 8.8: You can define a sequence using a piecewise formula.The following i...
 8.9: The numbers 1, 5, 12, 22, 35, 51, are calledpentagonal numbers beca...
 8.10: What conclusion can be drawn from the followinginformation about th...
 8.11: Let be the Fibonacci sequence.(a) Use mathematical induction to pro...
 8.12: The odds in favor of an event occurring are the ratioof the probabi...
 8.13: You are taking a test that contains only multiple choicequestions (...
 8.14: A dart is thrown at the circular target shown below. Thedart is equ...
 8.15: An event has possible outcomes, which have thevalues The probabilit...
Solutions for Chapter 8: Sequences, Series, and Probability
Full solutions for College Algebra  8th Edition
ISBN: 9781439048696
Solutions for Chapter 8: Sequences, Series, and Probability
Get Full SolutionsSince 109 problems in chapter 8: Sequences, Series, and Probability have been answered, more than 32929 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: College Algebra , edition: 8. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 8: Sequences, Series, and Probability includes 109 full stepbystep solutions. College Algebra was written by and is associated to the ISBN: 9781439048696.

Basis for V.
Independent vectors VI, ... , v d whose linear combinations give each vector in V as v = CIVI + ... + CdVd. V has many bases, each basis gives unique c's. A vector space has many bases!

Block matrix.
A matrix can be partitioned into matrix blocks, by cuts between rows and/or between columns. Block multiplication ofAB is allowed if the block shapes permit.

Cholesky factorization
A = CTC = (L.J]))(L.J]))T for positive definite A.

Cofactor Cij.
Remove row i and column j; multiply the determinant by (I)i + j •

Distributive Law
A(B + C) = AB + AC. Add then multiply, or mUltiply then add.

Hypercube matrix pl.
Row n + 1 counts corners, edges, faces, ... of a cube in Rn.

lAII = l/lAI and IATI = IAI.
The big formula for det(A) has a sum of n! terms, the cofactor formula uses determinants of size n  1, volume of box = I det( A) I.

Left nullspace N (AT).
Nullspace of AT = "left nullspace" of A because y T A = OT.

Matrix multiplication AB.
The i, j entry of AB is (row i of A)·(column j of B) = L aikbkj. By columns: Column j of AB = A times column j of B. By rows: row i of A multiplies B. Columns times rows: AB = sum of (column k)(row k). All these equivalent definitions come from the rule that A B times x equals A times B x .

Minimal polynomial of A.
The lowest degree polynomial with meA) = zero matrix. This is peA) = det(A  AI) if no eigenvalues are repeated; always meA) divides peA).

Normal matrix.
If N NT = NT N, then N has orthonormal (complex) eigenvectors.

Nullspace matrix N.
The columns of N are the n  r special solutions to As = O.

Outer product uv T
= column times row = rank one matrix.

Pseudoinverse A+ (MoorePenrose inverse).
The n by m matrix that "inverts" A from column space back to row space, with N(A+) = N(AT). A+ A and AA+ are the projection matrices onto the row space and column space. Rank(A +) = rank(A).

Rayleigh quotient q (x) = X T Ax I x T x for symmetric A: Amin < q (x) < Amax.
Those extremes are reached at the eigenvectors x for Amin(A) and Amax(A).

Schur complement S, D  C A } B.
Appears in block elimination on [~ g ].

Spectral Theorem A = QAQT.
Real symmetric A has real A'S and orthonormal q's.

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

Transpose matrix AT.
Entries AL = Ajj. AT is n by In, AT A is square, symmetric, positive semidefinite. The transposes of AB and AI are BT AT and (AT)I.

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