 9.2.1: What is an arithmetic sequence?
 9.2.2: How is the common difference of an arithmetic sequence found?
 9.2.3: How do we determine whether a sequence is arithmetic?
 9.2.4: What are the main differences between using a recursive formula and...
 9.2.5: Describe how linear functions and arithmetic sequences are similar....
 9.2.6: For the following exercises, find the common difference for the ari...
 9.2.7: For the following exercises, find the common difference for the ari...
 9.2.8: For the following exercises, determine whether the sequence is arit...
 9.2.9: For the following exercises, determine whether the sequence is arit...
 9.2.10: For the following exercises, write the first five terms of the arit...
 9.2.11: For the following exercises, write the first five terms of the arit...
 9.2.12: For the following exercises, write the first five terms of the arit...
 9.2.13: For the following exercises, write the first five terms of the arit...
 9.2.14: For the following exercises, find the specified term for the arithm...
 9.2.15: For the following exercises, find the specified term for the arithm...
 9.2.16: For the following exercises, find the specified term for the arithm...
 9.2.17: For the following exercises, find the specified term for the arithm...
 9.2.18: For the following exercises, find the specified term for the arithm...
 9.2.19: For the following exercises, find the first term given two terms fr...
 9.2.20: For the following exercises, find the first term given two terms fr...
 9.2.21: For the following exercises, find the first term given two terms fr...
 9.2.22: For the following exercises, find the first term given two terms fr...
 9.2.23: For the following exercises, find the first term given two terms fr...
 9.2.24: For the following exercises, find the specified term given two term...
 9.2.25: For the following exercises, find the specified term given two term...
 9.2.26: For the following exercises, use the recursive formula to write the...
 9.2.27: For the following exercises, use the recursive formula to write the...
 9.2.28: For the following exercises, write a recursive formula for each ari...
 9.2.29: For the following exercises, write a recursive formula for each ari...
 9.2.30: For the following exercises, write a recursive formula for each ari...
 9.2.31: For the following exercises, write a recursive formula for each ari...
 9.2.32: For the following exercises, write a recursive formula for each ari...
 9.2.33: For the following exercises, write a recursive formula for each ari...
 9.2.34: For the following exercises, write a recursive formula for each ari...
 9.2.35: For the following exercises, write a recursive formula for each ari...
 9.2.36: For the following exercises, write a recursive formula for each ari...
 9.2.37: For the following exercises, write a recursive formula for each ari...
 9.2.38: For the following exercises, use the recursive formula to write the...
 9.2.39: For the following exercises, use the recursive formula to write the...
 9.2.40: For the following exercises, use the recursive formula to write the...
 9.2.41: For the following exercises, use the recursive formula to write the...
 9.2.42: For the following exercises, use the recursive formula to write the...
 9.2.43: For the following exercises, write an explicit formula for each ari...
 9.2.44: For the following exercises, write an explicit formula for each ari...
 9.2.45: For the following exercises, write an explicit formula for each ari...
 9.2.46: For the following exercises, write an explicit formula for each ari...
 9.2.47: For the following exercises, write an explicit formula for each ari...
 9.2.48: For the following exercises, write an explicit formula for each ari...
 9.2.49: For the following exercises, write an explicit formula for each ari...
 9.2.50: For the following exercises, write an explicit formula for each ari...
 9.2.51: For the following exercises, write an explicit formula for each ari...
 9.2.52: For the following exercises, write an explicit formula for each ari...
 9.2.53: For the following exercises, find the number of terms in the given ...
 9.2.54: For the following exercises, find the number of terms in the given ...
 9.2.55: For the following exercises, find the number of terms in the given ...
 9.2.56: For the following exercises, determine whether the graph shown repr...
 9.2.57: For the following exercises, determine whether the graph shown repr...
 9.2.58: For the following exercises, use the information provided to graph ...
 9.2.59: For the following exercises, use the information provided to graph ...
 9.2.60: For the following exercises, use the information provided to graph ...
 9.2.61: For the following exercises, follow the steps to work with the arit...
 9.2.62: For the following exercises, follow the steps to work with the arit...
 9.2.63: For the following exercises, follow the steps to work with the arit...
 9.2.64: For the following exercises, follow the steps given above to work w...
 9.2.65: For the following exercises, follow the steps given above to work w...
 9.2.66: Give two examples of arithmetic sequences whose 4th terms are 9.
 9.2.67: Give two examples of arithmetic sequences whose 10th terms are 206.
 9.2.68: Find the 5th term of the arithmetic sequence {9b, 5b, b, }.
 9.2.69: Find the 11th term of the arithmetic sequence {3a 2b, a + 2b, a + 6...
 9.2.70: At which term does the sequence {5.4, 14.5, 23.6, ...} exceed 151?
 9.2.71: At which term does the sequence 17 _ 3 , 31 _ 6 , 14 _ 3 ,... b egi...
 9.2.72: For which terms does the finite arithmetic sequence 5 _ 2 , 19 ___ ...
 9.2.73: Write an arithmetic sequence using a recursive formula. Show the fi...
 9.2.74: Write an arithmetic sequence using an explicit formula. Show the fi...
Solutions for Chapter 9.2: ARITHMETIC SEQUENCES
Full solutions for College Algebra  1st Edition
ISBN: 9781938168383
Solutions for Chapter 9.2: ARITHMETIC SEQUENCES
Get Full SolutionsCollege Algebra was written by and is associated to the ISBN: 9781938168383. Chapter 9.2: ARITHMETIC SEQUENCES includes 74 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: College Algebra, edition: 1. Since 74 problems in chapter 9.2: ARITHMETIC SEQUENCES have been answered, more than 32095 students have viewed full stepbystep solutions from this chapter.

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.

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

Complete solution x = x p + Xn to Ax = b.
(Particular x p) + (x n in nullspace).

Conjugate Gradient Method.
A sequence of steps (end of Chapter 9) to solve positive definite Ax = b by minimizing !x T Ax  x Tb over growing Krylov subspaces.

Dimension of vector space
dim(V) = number of vectors in any basis for V.

Echelon matrix U.
The first nonzero entry (the pivot) in each row comes in a later column than the pivot in the previous row. All zero rows come last.

Elimination matrix = Elementary matrix Eij.
The identity matrix with an extra eij in the i, j entry (i # j). Then Eij A subtracts eij times row j of A from row i.

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

Fibonacci numbers
0,1,1,2,3,5, ... satisfy Fn = Fnl + Fn 2 = (A7 A~)I()q A2). Growth rate Al = (1 + .J5) 12 is the largest eigenvalue of the Fibonacci matrix [ } A].

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

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 .

Inverse matrix AI.
Square matrix with AI A = I and AAl = I. No inverse if det A = 0 and rank(A) < n and Ax = 0 for a nonzero vector x. The inverses of AB and AT are B1 AI and (AI)T. Cofactor formula (Al)ij = Cji! detA.

Iterative method.
A sequence of steps intended to approach the desired solution.

Jordan form 1 = M 1 AM.
If A has s independent eigenvectors, its "generalized" eigenvector matrix M gives 1 = diag(lt, ... , 1s). The block his Akh +Nk where Nk has 1 's on diagonall. Each block has one eigenvalue Ak and one eigenvector.

Least squares solution X.
The vector x that minimizes the error lie 112 solves AT Ax = ATb. Then e = b  Ax is orthogonal to all columns of A.

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

Row space C (AT) = all combinations of rows of A.
Column vectors by convention.

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

Singular Value Decomposition
(SVD) A = U:E VT = (orthogonal) ( diag)( orthogonal) First r columns of U and V are orthonormal bases of C (A) and C (AT), AVi = O'iUi with singular value O'i > O. Last columns are orthonormal bases of nullspaces.

Tridiagonal matrix T: tij = 0 if Ii  j I > 1.
T 1 has rank 1 above and below diagonal.