 61.1: Nichelle said that sequence of numbers in which each term equals ha...
 61.2: a. Jacob said that if an 5 3n 2 1, then an11 5 an 1 3. Do you agree...
 61.3: In 318, write the first five terms of each sequence. an 5 n
 61.4: In 318, write the first five terms of each sequence. an 5 n 1 5
 61.5: In 318, write the first five terms of each sequence. an 5 2n
 61.6: In 318, write the first five terms of each sequence. an 5
 61.7: In 318, write the first five terms of each sequence. an 5
 61.8: In 318, write the first five terms of each sequence. an 5 20 2 n
 61.9: In 318, write the first five terms of each sequence. an 5 3n
 61.10: In 318, write the first five terms of each sequence. an 5 n2
 61.11: In 318, write the first five terms of each sequence. an 5 2n 1 3
 61.12: In 318, write the first five terms of each sequence. an 5 2n 2 1
 61.13: In 318, write the first five terms of each sequence. an 5
 61.14: In 318, write the first five terms of each sequence. an 5
 61.15: In 318, write the first five terms of each sequence. an 5 2n
 61.16: In 318, write the first five terms of each sequence. an 5 12 2 3n
 61.17: In 318, write the first five terms of each sequence. an 5
 61.18: In 318, write the first five terms of each sequence. an 5 1 i
 61.19: In 1930: a. Write an algebraic expression that represents an for ea...
 61.20: In 1930: a. Write an algebraic expression that represents an for ea...
 61.21: In 1930: a. Write an algebraic expression that represents an for ea...
 61.22: In 1930: a. Write an algebraic expression that represents an for ea...
 61.23: In 1930: a. Write an algebraic expression that represents an for ea...
 61.24: In 1930: a. Write an algebraic expression that represents an for ea...
 61.25: In 1930: a. Write an algebraic expression that represents an for ea...
 61.26: In 1930: a. Write an algebraic expression that represents an for ea...
 61.27: In 1930: a. Write an algebraic expression that represents an for ea...
 61.28: In 1930: a. Write an algebraic expression that represents an for ea...
 61.29: In 1930: a. Write an algebraic expression that represents an for ea...
 61.30: In 1930: a. Write an algebraic expression that represents an for ea...
 61.31: In 3139, write the first five terms of each sequence. a1 5 5, an = ...
 61.32: In 3139, write the first five terms of each sequence. a1 5 1, an11 ...
 61.33: In 3139, write the first five terms of each sequence. a1 5 1, an 5 ...
 61.34: In 3139, write the first five terms of each sequence. a1 5 22, an 5...
 61.35: In 3139, write the first five terms of each sequence. a1 5 20, an 5...
 61.36: In 3139, write the first five terms of each sequence. a1 5 4, an11 ...
 61.37: In 3139, write the first five terms of each sequence. a2 5 36, an 5
 61.38: In 3139, write the first five terms of each sequence. a3 5 25, an11...
 61.39: In 3139, write the first five terms of each sequence. a5 5 , an 5
 61.40: Sean has started an exercise program. The first day he worked out f...
 61.41: Sherri wants to increase her vocabulary. On Monday she learned the ...
 61.42: Julie is trying to lose weight. She now weighs 180 pounds. Every we...
 61.43: January 1, 2008, was a Tuesday. a. List the dates for each Tuesday ...
 61.44: Hui started a new job with a weekly salary of $400. After one year,...
 61.45: One of the most famous sequences is the Fibonacci sequence. In this...
Solutions for Chapter 61: Sequences
Full solutions for Amsco's Algebra 2 and Trigonometry  1st Edition
ISBN: 9781567657029
Solutions for Chapter 61: Sequences
Get Full SolutionsAmsco's Algebra 2 and Trigonometry was written by and is associated to the ISBN: 9781567657029. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Amsco's Algebra 2 and Trigonometry, edition: 1. Chapter 61: Sequences includes 45 full stepbystep solutions. Since 45 problems in chapter 61: Sequences have been answered, more than 28698 students have viewed full stepbystep solutions from this chapter.

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!

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.

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.

Column picture of Ax = b.
The vector b becomes a combination of the columns of A. The system is solvable only when b is in the column space C (A).

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.

Cyclic shift
S. Permutation with S21 = 1, S32 = 1, ... , finally SIn = 1. Its eigenvalues are the nth roots e2lrik/n of 1; eigenvectors are columns of the Fourier matrix F.

Diagonal matrix D.
dij = 0 if i # j. Blockdiagonal: zero outside square blocks Du.

Eigenvalue A and eigenvector x.
Ax = AX with x#O so det(A  AI) = o.

Krylov subspace Kj(A, b).
The subspace spanned by b, Ab, ... , AjIb. Numerical methods approximate A I b by x j with residual b  Ax j in this subspace. A good basis for K j requires only multiplication by A at each step.

Linear combination cv + d w or L C jV j.
Vector addition and scalar multiplication.

Matrix multiplication AB.
The i, j entry of AB is (row i of A)ยท(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 .

Multiplicities AM and G M.
The algebraic multiplicity A M of A is the number of times A appears as a root of det(A  AI) = O. The geometric multiplicity GM is the number of independent eigenvectors for A (= dimension of the eigenspace).

Projection p = a(aTblaTa) onto the line through a.
P = aaT laTa has rank l.

Rank one matrix A = uvT f=. O.
Column and row spaces = lines cu and cv.

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

Symmetric matrix A.
The transpose is AT = A, and aU = a ji. AI is also symmetric.

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.

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

Vector addition.
v + w = (VI + WI, ... , Vn + Wn ) = diagonal of parallelogram.

Vector space V.
Set of vectors such that all combinations cv + d w remain within V. Eight required rules are given in Section 3.1 for scalars c, d and vectors v, w.