 116.1: Let b n be the balance left on Mariselas loan after n months. Write...
 116.2: What percent of Mariselas loan remains to be paid after half a year?
 116.3: Extend the spreadsheet to the whole year. What is the balance after...
 116.4: Suppose Marisela decides to pay $50 every month. How long would it ...
 116.5: Suppose that, based on how much she can afford, Marisela will pay a...
 116.6: Jamie has a threeyear, $12,000 car loan. The annual interest rate ...
 116.7: f(x) = 3x  4, x 0 = 3
 116.8: f(x) = 2x + 5, x 0 = 2
 116.9: f(x) = x 2 + 2, x 0 = 1
 116.10: a 1 = 6, a n + 1 = a n + 3
 116.11: a 1 = 13, a n + 1 = a n + 5
 116.12: a 1 = 2, a n + 1 = a n  n
 116.13: a 1 = 6, a n + 1 = a n + n + 3
 116.14: a 1 = 9, a n + 1 = 2 a n  4
 116.15: a 1 = 4, a n + 1 = 3 a n  6
 116.16: If a 0 = 7 and a n + 1 = a n + 12 for n 0, find the value of a 5 .
 116.17: If a 0 = 1 and a n + 1 = 2.1 for n 0, then what is the value of a 4 ?
 116.18: f(x) = 9x  2, x 0 = 2
 116.19: f(x) = 4x  3, x 0 = 2
 116.20: f(x) = 3x + 5, x 0 = 4
 116.21: f(x) = 5x + 1, x 0 = 1
 116.22: Write the sequence of the lengths of the sides of the squares you a...
 116.23: Write a recursive formula for the sequence of lengths added.
 116.24: Identify the sequence in Exercise 23.
 116.25: Write a sequence of the first five triangular numbers.
 116.26: Write a recursive formula for the nth triangular number t n
 116.27: What is the 200th triangular number?
 116.28: LOANS Miguels monthly car payment is $234.85. The recursive formula...
 116.29: ECONOMICS If the rate of inflation is 2%, the cost of an item in fu...
 116.30: f(x) = 2 x 2  5, x 0 = 1 3
 116.31: f(x) = 3 x 2  4, x 0 = 1
 116.32: f(x) = 2 x 2 + 2x + 1, x 0 = _1
 116.33: f(x) = 3 x 2  3x + 2, x 0 = _1 3
 116.34: OPEN ENDED Write a recursive formula for a sequence whose first thr...
 116.35: REASONING Is the statement x n x n  1 sometimes, always, or never ...
 116.36: CHALLENGE Are there a function f(x) and an initial value x 0 such t...
 116.37: Writing in Math Use the information on page 658 to explain how the ...
 116.38: ACT/SAT The figure is made of three concentric semicircles. What is...
 116.39: REVIEW If x is a real number, for what values of x is the equation ...
 116.40: 9 + 6 + 4 + ... 4
 116.41: 1 8 + _1 32 + _1 128 + ...
 116.42: 4  _8 3 + _16 9 + ...
 116.43: 2  10 + 50  ... to 6 terms 4
 116.44: 3 + 1 + _1 3 + ... to 7 terms
 116.45: GEOMETRY The area of rectangle ABCD is 6 x 2 + 38x + 56 square unit...
 116.46: 5 4 3 2 1 4
 116.47: 4 3 2 1
 116.48: 9 8 7 6 4 3 2 1
Solutions for Chapter 116: Recursion and Special Sequences
Full solutions for Algebra 2, Student Edition (MERRILL ALGEBRA 2)  1st Edition
ISBN: 9780078738302
Solutions for Chapter 116: Recursion and Special Sequences
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Algebra 2, Student Edition (MERRILL ALGEBRA 2), edition: 1. Algebra 2, Student Edition (MERRILL ALGEBRA 2) was written by and is associated to the ISBN: 9780078738302. Chapter 116: Recursion and Special Sequences includes 48 full stepbystep solutions. Since 48 problems in chapter 116: Recursion and Special Sequences have been answered, more than 61378 students have viewed full stepbystep solutions from this chapter.

Affine transformation
Tv = Av + Vo = linear transformation plus shift.

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.

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

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

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.

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

Hermitian matrix A H = AT = A.
Complex analog a j i = aU of a symmetric matrix.

Network.
A directed graph that has constants Cl, ... , Cm associated with the edges.

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.

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

Particular solution x p.
Any solution to Ax = b; often x p has free variables = o.

Pascal matrix
Ps = pascal(n) = the symmetric matrix with binomial entries (i1~;2). Ps = PL Pu all contain Pascal's triangle with det = 1 (see Pascal in the index).

Plane (or hyperplane) in Rn.
Vectors x with aT x = O. Plane is perpendicular to a =1= O.

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

Reflection matrix (Householder) Q = I 2uuT.
Unit vector u is reflected to Qu = u. All x intheplanemirroruTx = o have Qx = x. Notice QT = Q1 = Q.

Saddle point of I(x}, ... ,xn ).
A point where the first derivatives of I are zero and the second derivative matrix (a2 II aXi ax j = Hessian matrix) is indefinite.

Semidefinite matrix A.
(Positive) semidefinite: all x T Ax > 0, all A > 0; A = any RT R.

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

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

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