 113.1: Find the next two terms of the geometric sequence 20, 30, 45, .
 113.2: Find the first five terms of the geometric sequence for which a 1 =...
 113.3: STANDARDIZED TEST PRACTICE What is the missing term in the geometri...
 113.4: Find a 9 for the geometric sequence 60, 30, 15, .
 113.5: Find a 8 for the geometric sequence _1 8 , _1 4 , _1 2 , .
 113.6: a 1 = 7, r = 2, n = 4
 113.7: a 1 = 3, r = _1 3 , n = 5
 113.8: Write an equation for the nth term of the geometric sequence 4, 8, ...
 113.9: Write an equation for the nth term of the geometric sequence 15, 5,...
 113.10: a 3 = 24, r = _1 2 , n = 7
 113.11: a 3 = 32, r = 0.5, n = 6
 113.12: Find two geometric means between 1 and 27.
 113.13: Find two geometric means between 2 and 54.
 113.14: 405, 135, 45,
 113.15: 81, 108, 144,
 113.16: 16, 24, 36,
 113.17: 162, 108, 72,
 113.18: a 1 = 2, r = 3
 113.19: a 1 = 1, r = 4 20. Find a 7 if a 1 = 12 and r = _1 2 . 21. Find a 6...
 113.20: Find a 7 if a 1 = 12 and r = _1 2 .
 113.21: Find a 6 if a 1 = _1 3 and r = 6.
 113.22: INTEREST An investment pays interest so that each year the value of...
 113.23: SALARIES Geraldos current salary is $40,000 per year. His annual pa...
 113.24: a 1 = _1 3 , r = 3, n = 8
 113.25: a 1 = _1 64, r = 4, n = 9
 113.26: a 9 for a 1 = _1 5 , 1, 5,
 113.27: a 7 for _1 32, _1 16, _1 8 ,
 113.28: a 4 = 16, r = 0.5, n = 8
 113.29: a 6 = 3, r = 2, n = 12
 113.30: 36, 12, 4,
 113.31: 64, 16, 4,
 113.32: 2, 10, 50,
 113.33: 4, 12, 36,
 113.34: 9, ? , ? , ? , 144
 113.35: 4, ? , ? , ? , 324
 113.36: 32, ? , ? , ? , ? , 1 3
 113.37: 3, ? , ? , ? , ? , 96
 113.38: 5 2 , _5 3 , _10 9 ,
 113.39: 1 3 , _5 6 , _25 12 ,
 113.40: 1.25, 1.5, 1.8,
 113.41: 1.4, 3.5, 8.75,
 113.42: a 1 = 243, r = _1 3
 113.43: a 1 = 576, r =  _1 2
 113.44: ART A oneton ice sculpture is melting so that it loses oneeighth ...
 113.45: RESEARCH Use the Internet or other resource to find the halflife o...
 113.46: How much of an 80milligram sample of Iodine131 would be left afte...
 113.47: a 1 = 16,807, r = _3 7 , n = 6
 113.48: a 1 = 4096, r = _1 4 , n = 8
 113.49: a 8 for 4, 12, 36,
 113.50: a 6 for 540, 90, 15,
 113.51: a 4 = 50, r = 2, n = 8
 113.52: a 4 = 1, r = 3, n = 10
 113.53: OPEN ENDED Write a geometric sequence with a common ratio of _2 3
 113.54: FIND THE ERROR Marika and Lori are finding the seventh term of the ...
 113.55: Which One Doesnt Belong? Identify the sequence that does not belong...
 113.56: Every sequence is either arithmetic or geometric.
 113.57: There is no sequence that is both arithmetic and geometric.
 113.58: Writing in Math Use the information on pages 636 and 637 to explain...
 113.59: ACT/SAT The first four terms of a geometric sequence are shown in t...
 113.60: REVIEW The table shows the cost of jelly beans depending on the amo...
 113.61: a 1 = 11, a n = 44, n = 23
 113.62: a 1 = 5, d = 3, n = 14
 113.63: 15, ? , ? , 27
 113.64: 8, ? , ? , ? , 24
 113.65: GEOMETRY Find the perimeter of a triangle with vertices at (2, 4), ...
 113.66: 1  2 _7 1  2
 113.67: 1  (_1 2) 6 _ 1  _1 2
 113.68: 1  ( _1 3) 5 _ 1  ( _1 3)
Solutions for Chapter 113: Geometric Sequences
Full solutions for Algebra 2, Student Edition (MERRILL ALGEBRA 2)  1st Edition
ISBN: 9780078738302
Solutions for Chapter 113: Geometric Sequences
Get Full SolutionsChapter 113: Geometric Sequences includes 68 full stepbystep solutions. This textbook survival guide was created for the textbook: Algebra 2, Student Edition (MERRILL ALGEBRA 2), edition: 1. This expansive textbook survival guide covers the following chapters and their solutions. Since 68 problems in chapter 113: Geometric Sequences have been answered, more than 53664 students have viewed full stepbystep solutions from this chapter. Algebra 2, Student Edition (MERRILL ALGEBRA 2) was written by and is associated to the ISBN: 9780078738302.

Augmented matrix [A b].
Ax = b is solvable when b is in the column space of A; then [A b] has the same rank as A. Elimination on [A b] keeps equations correct.

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.

Cross product u xv in R3:
Vector perpendicular to u and v, length Ilullllvlll sin el = area of parallelogram, u x v = "determinant" of [i j k; UI U2 U3; VI V2 V3].

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].

Free columns of A.
Columns without pivots; these are combinations of earlier columns.

Lucas numbers
Ln = 2,J, 3, 4, ... satisfy Ln = L n l +Ln 2 = A1 +A~, with AI, A2 = (1 ± /5)/2 from the Fibonacci matrix U~]' Compare Lo = 2 with Fo = O.

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).

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

Nilpotent matrix N.
Some power of N is the zero matrix, N k = o. The only eigenvalue is A = 0 (repeated n times). Examples: triangular matrices with zero diagonal.

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

Orthogonal subspaces.
Every v in V is orthogonal to every w in W.

Partial pivoting.
In each column, choose the largest available pivot to control roundoff; all multipliers have leij I < 1. See condition number.

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

Random matrix rand(n) or randn(n).
MATLAB creates a matrix with random entries, uniformly distributed on [0 1] for rand and standard normal distribution for randn.

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.

Schwarz inequality
Iv·wl < IIvll IIwll.Then IvTAwl2 < (vT Av)(wT Aw) for pos def A.

Standard basis for Rn.
Columns of n by n identity matrix (written i ,j ,k in R3).

Vector v in Rn.
Sequence of n real numbers v = (VI, ... , Vn) = point in Rn.

Wavelets Wjk(t).
Stretch and shift the time axis to create Wjk(t) = woo(2j t  k).