 11.3.1: A sequence in which each term after the first is obtained by multip...
 11.3.2: The nth term of the sequence described in Concept Check 1 is given ...
 11.3.3: The sum, Sn, of the first n terms of the sequence described in Conc...
 11.3.4: A sequence of equal payments made at equal time periods is called a...
 11.3.5: An infinite sum of the form a1 + a1r + a1r2 + a1r3 + g is called a/...
 11.3.6: The first four terms of a 6 i=1 2i are ____________, ____________, ...
 11.3.7: Determine whether each sequence is arithmetic or geometric.4, 8, 12...
 11.3.8: Determine whether each sequence is arithmetic or geometric.4, 8, 16...
 11.3.9: Determine whether each sequence is arithmetic or geometric.1, 3, 9...
 11.3.10: Determine whether each sequence is arithmetic or geometric.1, 1, 3...
 11.3.11: In Exercises 916, write the first five terms of each geometric sequ...
 11.3.12: In Exercises 916, write the first five terms of each geometric sequ...
 11.3.13: In Exercises 916, write the first five terms of each geometric sequ...
 11.3.14: In Exercises 916, write the first five terms of each geometric sequ...
 11.3.15: In Exercises 916, write the first five terms of each geometric sequ...
 11.3.16: In Exercises 916, write the first five terms of each geometric sequ...
 11.3.17: In Exercises 1724, use the formula for the general term (the nth te...
 11.3.18: In Exercises 1724, use the formula for the general term (the nth te...
 11.3.19: In Exercises 1724, use the formula for the general term (the nth te...
 11.3.20: In Exercises 1724, use the formula for the general term (the nth te...
 11.3.21: In Exercises 1724, use the formula for the general term (the nth te...
 11.3.22: In Exercises 1724, use the formula for the general term (the nth te...
 11.3.23: In Exercises 1724, use the formula for the general term (the nth te...
 11.3.24: In Exercises 1724, use the formula for the general term (the nth te...
 11.3.25: In Exercises 2532, write a formula for the general term (the nth te...
 11.3.26: In Exercises 2532, write a formula for the general term (the nth te...
 11.3.27: In Exercises 2532, write a formula for the general term (the nth te...
 11.3.28: In Exercises 2532, write a formula for the general term (the nth te...
 11.3.29: In Exercises 2532, write a formula for the general term (the nth te...
 11.3.30: In Exercises 2532, write a formula for the general term (the nth te...
 11.3.31: In Exercises 2532, write a formula for the general term (the nth te...
 11.3.32: In Exercises 2532, write a formula for the general term (the nth te...
 11.3.33: Use the formula for the sum of the first n terms of a geometric seq...
 11.3.34: Use the formula for the sum of the first n terms of a geometric seq...
 11.3.35: Use the formula for the sum of the first n terms of a geometric seq...
 11.3.36: Use the formula for the sum of the first n terms of a geometric seq...
 11.3.37: Use the formula for the sum of the first n terms of a geometric seq...
 11.3.38: Use the formula for the sum of the first n terms of a geometric seq...
 11.3.39: In Exercises 3944, find the indicated sum. Use the formula for the ...
 11.3.40: In Exercises 3944, find the indicated sum. Use the formula for the ...
 11.3.41: In Exercises 3944, find the indicated sum. Use the formula for the ...
 11.3.42: In Exercises 3944, find the indicated sum. Use the formula for the ...
 11.3.43: In Exercises 3944, find the indicated sum. Use the formula for the ...
 11.3.44: In Exercises 3944, find the indicated sum. Use the formula for the ...
 11.3.45: In Exercises 4552, find the sum of each infinite geometric series.1...
 11.3.46: In Exercises 4552, find the sum of each infinite geometric series.1...
 11.3.47: In Exercises 4552, find the sum of each infinite geometric series.....
 11.3.48: In Exercises 4552, find the sum of each infinite geometric series.5...
 11.3.49: In Exercises 4552, find the sum of each infinite geometric series.1...
 11.3.50: In Exercises 4552, find the sum of each infinite geometric series.3...
 11.3.51: In Exercises 4552, find the sum of each infinite geometric series.a...
 11.3.52: In Exercises 4552, find the sum of each infinite geometric series.a...
 11.3.53: In Exercises 5358, express each repeating decimal as a fraction in ...
 11.3.54: In Exercises 5358, express each repeating decimal as a fraction in ...
 11.3.55: In Exercises 5358, express each repeating decimal as a fraction in ...
 11.3.56: In Exercises 5358, express each repeating decimal as a fraction in ...
 11.3.57: In Exercises 5358, express each repeating decimal as a fraction in ...
 11.3.58: In Exercises 5358, express each repeating decimal as a fraction in ...
 11.3.59: In Exercises 5964, the general term of a sequence is given. Determi...
 11.3.60: In Exercises 5964, the general term of a sequence is given. Determi...
 11.3.61: In Exercises 5964, the general term of a sequence is given. Determi...
 11.3.62: In Exercises 5964, the general term of a sequence is given. Determi...
 11.3.63: In Exercises 5964, the general term of a sequence is given. Determi...
 11.3.64: In Exercises 5964, the general term of a sequence is given. Determi...
 11.3.65: In Exercises 6570, let {an} = 5, 10, 20, 40,c, {bn} = 10, 5, 20...
 11.3.66: In Exercises 6570, let {an} = 5, 10, 20, 40,c, {bn} = 10, 5, 20...
 11.3.67: In Exercises 6570, let {an} = 5, 10, 20, 40,c, {bn} = 10, 5, 20...
 11.3.68: In Exercises 6570, let {an} = 5, 10, 20, 40,c, {bn} = 10, 5, 20...
 11.3.69: In Exercises 6570, let {an} = 5, 10, 20, 40,c, {bn} = 10, 5, 20...
 11.3.70: In Exercises 6570, let {an} = 5, 10, 20, 40,c, {bn} = 10, 5, 20...
 11.3.71: In Exercises 7172, find a2 and a3 for each geometric sequence.8, a2...
 11.3.72: In Exercises 7172, find a2 and a3 for each geometric sequence.2, a2...
 11.3.73: In Exercises 7374, round all answers to the nearest dollar.Here are...
 11.3.74: In Exercises 7374, round all answers to the nearest dollar.Here are...
 11.3.75: Use the formula for the general term (the nth term) of a geometric ...
 11.3.76: Use the formula for the general term (the nth term) of a geometric ...
 11.3.77: Use the formula for the general term (the nth term) of a geometric ...
 11.3.78: Use the formula for the general term (the nth term) of a geometric ...
 11.3.79: In Exercises 7980, you will develop geometric sequences that model ...
 11.3.80: In Exercises 7980, you will develop geometric sequences that model ...
 11.3.81: Use the formula for the sum of the first n terms of a geometric seq...
 11.3.82: Use the formula for the sum of the first n terms of a geometric seq...
 11.3.83: Use the formula for the sum of the first n terms of a geometric seq...
 11.3.84: Use the formula for the sum of the first n terms of a geometric seq...
 11.3.85: Use the formula for the sum of the first n terms of a geometric seq...
 11.3.86: Use the formula for the sum of the first n terms of a geometric seq...
 11.3.87: Use the formula for the value of an annuity to solve Exercises 8792...
 11.3.88: Use the formula for the value of an annuity to solve Exercises 8792...
 11.3.89: Use the formula for the value of an annuity to solve Exercises 8792...
 11.3.90: Use the formula for the value of an annuity to solve Exercises 8792...
 11.3.91: Use the formula for the value of an annuity to solve Exercises 8792...
 11.3.92: Use the formula for the value of an annuity to solve Exercises 8792...
 11.3.93: Use the formula for the sum of an infinite geometric series to solv...
 11.3.94: Use the formula for the sum of an infinite geometric series to solv...
 11.3.95: Use the formula for the sum of an infinite geometric series to solv...
 11.3.96: What is a geometric sequence? Give an example with your explanation.
 11.3.97: What is the common ratio in a geometric sequence?
 11.3.98: Explain how to find the general term of a geometric sequence
 11.3.99: Explain how to find the sum of the first n terms of a geometric seq...
 11.3.100: What is an annuity?
 11.3.101: What is the difference between a geometric sequence and an infinite...
 11.3.102: How do you determine if an infinite geometric series has a sum? Exp...
 11.3.103: Would you rather have $10,000,000 and a brand new BMW or 1 today, 2...
 11.3.104: For the first 30 days of a flu outbreak, the number of students on ...
 11.3.105: . Use the SEQ (sequence) capability of a graphing utility and the f...
 11.3.106: Use the capability of a graphing utility to calculate the sum of a ...
 11.3.107: In Exercises 107108, use a graphing utility to graph the function. ...
 11.3.108: In Exercises 107108, use a graphing utility to graph the function. ...
 11.3.109: Make Sense? In Exercises 109112, determine whether each statement m...
 11.3.110: Make Sense? In Exercises 109112, determine whether each statement m...
 11.3.111: Make Sense? In Exercises 109112, determine whether each statement m...
 11.3.112: Make Sense? In Exercises 109112, determine whether each statement m...
 11.3.113: In Exercises 113116, determine whether each statement is true or fa...
 11.3.114: In Exercises 113116, determine whether each statement is true or fa...
 11.3.115: In Exercises 113116, determine whether each statement is true or fa...
 11.3.116: In Exercises 113116, determine whether each statement is true or fa...
 11.3.117: In a pesteradication program, sterilized male flies are released i...
 11.3.118: You are now 25 years old and would like to retire at age 55 with a ...
 11.3.119: Simplify: 228  327 + 263. (Section 7.4, Example 2)
 11.3.120: Solve: 2x2 = 4  x. (Section 8.2, Example 2)
 11.3.121: Rationalize the denominator: 6 23  25 . (Section 7.5, Example 5)
 11.3.122: Exercises 122124 will help you prepare for the material covered in ...
 11.3.123: Exercises 122124 will help you prepare for the material covered in ...
 11.3.124: Exercises 122124 will help you prepare for the material covered in ...
Solutions for Chapter 11.3: Geometric Sequences and Series
Full solutions for Intermediate Algebra for College Students  6th Edition
ISBN: 9780321758934
Solutions for Chapter 11.3: Geometric Sequences and Series
Get Full SolutionsIntermediate Algebra for College Students was written by and is associated to the ISBN: 9780321758934. Chapter 11.3: Geometric Sequences and Series includes 124 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. Since 124 problems in chapter 11.3: Geometric Sequences and Series have been answered, more than 26347 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Intermediate Algebra for College Students, edition: 6.

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

Commuting matrices AB = BA.
If diagonalizable, they share n eigenvectors.

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

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

Free variable Xi.
Column i has no pivot in elimination. We can give the n  r free variables any values, then Ax = b determines the r pivot variables (if solvable!).

Kronecker product (tensor product) A ® B.
Blocks aij B, eigenvalues Ap(A)Aq(B).

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

Pseudoinverse A+ (MoorePenrose inverse).
The n by m matrix that "inverts" A from column space back to row space, with N(A+) = N(AT). A+ A and AA+ are the projection matrices onto the row space and column space. Rank(A +) = rank(A).

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

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.

Right inverse A+.
If A has full row rank m, then A+ = AT(AAT)l has AA+ = 1m.

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

Simplex method for linear programming.
The minimum cost vector x * is found by moving from comer to lower cost comer along the edges of the feasible set (where the constraints Ax = b and x > 0 are satisfied). Minimum cost at a comer!

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.

Skewsymmetric matrix K.
The transpose is K, since Kij = Kji. Eigenvalues are pure imaginary, eigenvectors are orthogonal, eKt is an orthogonal matrix.

Spanning set.
Combinations of VI, ... ,Vm fill the space. The columns of A span C (A)!

Stiffness matrix
If x gives the movements of the nodes, K x gives the internal forces. K = ATe A where C has spring constants from Hooke's Law and Ax = stretching.

Toeplitz matrix.
Constant down each diagonal = timeinvariant (shiftinvariant) filter.

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

Unitary matrix UH = U T = UI.
Orthonormal columns (complex analog of Q).