 8.2.59: In Exercises 5966, find the indicated th partial sum of thearithmet...
 8.2.60: In Exercises 5966, find the indicated th partial sum of thearithmet...
 8.2.61: In Exercises 5966, find the indicated th partial sum of thearithmet...
 8.2.62: In Exercises 5966, find the indicated th partial sum of thearithmet...
 8.2.63: In Exercises 5966, find the indicated th partial sum of thearithmet...
 8.2.64: In Exercises 5966, find the indicated th partial sum of thearithmet...
 8.2.65: In Exercises 5966, find the indicated th partial sum of thearithmet...
 8.2.66: In Exercises 5966, find the indicated th partial sum of thearithmet...
 8.2.67: In Exercises 6774, find the partial sum.
 8.2.68: In Exercises 6774, find the partial sum.
 8.2.69: In Exercises 6774, find the partial sum.
 8.2.70: In Exercises 6774, find the partial sum.
 8.2.71: In Exercises 6774, find the partial sum.
 8.2.72: In Exercises 6774, find the partial sum.
 8.2.73: In Exercises 6774, find the partial sum.
 8.2.74: In Exercises 6774, find the partial sum.
 8.2.75: In Exercises 7578, match the arithmetic sequence with itsgraph. [Th...
 8.2.76: In Exercises 7578, match the arithmetic sequence with itsgraph. [Th...
 8.2.77: In Exercises 7578, match the arithmetic sequence with itsgraph. [Th...
 8.2.78: In Exercises 7578, match the arithmetic sequence with itsgraph. [Th...
 8.2.79: In Exercises 7982, use a graphing utility to graph the first 10term...
 8.2.80: In Exercises 7982, use a graphing utility to graph the first 10term...
 8.2.81: In Exercises 7982, use a graphing utility to graph the first 10term...
 8.2.82: In Exercises 7982, use a graphing utility to graph the first 10term...
 8.2.83: In Exercises 8388, use a graphing utility to find the partialsum.20...
 8.2.84: In Exercises 8388, use a graphing utility to find the partialsum.50...
 8.2.85: In Exercises 8388, use a graphing utility to find the partialsum.10...
 8.2.86: In Exercises 8388, use a graphing utility to find the partialsum. 1...
 8.2.87: In Exercises 8388, use a graphing utility to find the partialsum. 6...
 8.2.88: In Exercises 8388, use a graphing utility to find the partialsum. 2...
 8.2.89: JOB OFFER In Exercises 89 and 90, consider a job offerwith the give...
 8.2.90: JOB OFFER In Exercises 89 and 90, consider a job offerwith the give...
 8.2.91: SEATING CAPACITY Determine the seating capacityof an auditorium wit...
 8.2.92: SEATING CAPACITY Determine the seating capacityof an auditorium wit...
 8.2.93: BRICK PATTERN A brick patio has the approximateshape of a trapezoid...
 8.2.94: BRICK PATTERN A triangular brick wall is made bycutting some bricks...
 8.2.95: FALLING OBJECT An object with negligible airresistance is dropped f...
 8.2.96: FALLING OBJECT An object with negligible airresistance is dropped f...
 8.2.97: PRIZE MONEY A county fair is holding a bakedgoods competition in wh...
 8.2.98: PRIZE MONEY A city bowling league is holdinga tournament in which t...
 8.2.99: TOTAL PROFIT A small snowplowing companymakes a profit of $8000 dur...
 8.2.100: TOTAL SALES An entrepreneur sells $15,000 worthof sports memorabili...
 8.2.101: BORROWING MONEY You borrowed $2000 from afriend to purchase a new l...
 8.2.102: BORROWING MONEY You borrowed $5000 fromyour parents to purchase a u...
 8.2.103: DATA ANALYSIS: PERSONAL INCOME The tableshows the per capita person...
 8.2.104: DATA ANALYSIS: SALES The table shows the sales(in billions of dolla...
 8.2.105: TRUE OR FALSE? In Exercises 105 and 106, determinewhether the state...
 8.2.106: TRUE OR FALSE? In Exercises 105 and 106, determinewhether the state...
 8.2.107: In Exercises 107 and 108, find the first 10 terms of thesequence.a1...
 8.2.108: In Exercises 107 and 108, find the first 10 terms of thesequence. a...
 8.2.109: WRITING Explain how to use the first two terms ofan arithmetic sequ...
 8.2.110: CAPSTONE In your own words, describe thecharacteristics of an arith...
 8.2.111: (a) Graph the first 10 terms of the arithmetic sequence(b) Graph th...
 8.2.112: PATTERN RECOGNITION(a) Compute the following sums of consecutivepos...
 8.2.113: THINK ABOUT IT The sum of the first 20 terms ofan arithmetic sequen...
 8.2.114: THINK ABOUT IT The sum of the first terms of anarithmetic sequence ...
Solutions for Chapter 8.2: Arithmetic Sequences and Partial Sums
Full solutions for College Algebra  8th Edition
ISBN: 9781439048696
Solutions for Chapter 8.2: Arithmetic Sequences and Partial Sums
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. College Algebra was written by and is associated to the ISBN: 9781439048696. Chapter 8.2: Arithmetic Sequences and Partial Sums includes 56 full stepbystep solutions. Since 56 problems in chapter 8.2: Arithmetic Sequences and Partial Sums have been answered, more than 33334 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: College Algebra , edition: 8.

Associative Law (AB)C = A(BC).
Parentheses can be removed to leave ABC.

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

Circulant matrix C.
Constant diagonals wrap around as in cyclic shift S. Every circulant is Col + CIS + ... + Cn_lSn  l . Cx = convolution c * x. Eigenvectors in F.

Column space C (A) =
space of all combinations of the columns of A.

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).

Complex conjugate
z = a  ib for any complex number z = a + ib. Then zz = Iz12.

Factorization
A = L U. If elimination takes A to U without row exchanges, then the lower triangular L with multipliers eij (and eii = 1) brings U back to A.

Fast Fourier Transform (FFT).
A factorization of the Fourier matrix Fn into e = log2 n matrices Si times a permutation. Each Si needs only nl2 multiplications, so Fnx and Fn1c can be computed with ne/2 multiplications. Revolutionary.

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

Incidence matrix of a directed graph.
The m by n edgenode incidence matrix has a row for each edge (node i to node j), with entries 1 and 1 in columns i and j .

Indefinite matrix.
A symmetric matrix with eigenvalues of both signs (+ and  ).

Length II x II.
Square root of x T x (Pythagoras in n dimensions).

Linearly dependent VI, ... , Vn.
A combination other than all Ci = 0 gives L Ci Vi = O.

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 .

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

Orthogonal matrix Q.
Square matrix with orthonormal columns, so QT = Ql. Preserves length and angles, IIQxll = IIxll and (QX)T(Qy) = xTy. AlllAI = 1, with orthogonal eigenvectors. Examples: Rotation, reflection, permutation.

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).

Similar matrices A and B.
Every B = MI AM has the same eigenvalues as A.

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

Volume of box.
The rows (or the columns) of A generate a box with volume I det(A) I.