 11.2.1: A sequence in which each term after the first differs from the prec...
 11.2.2: The nth term of the sequence described in Concept Check 1 is given ...
 11.2.3: The sum, Sn, of the first n terms of the sequence described in Conc...
 11.2.4: The first term of a 20 i=1 (6i  4) is ______________ and the last ...
 11.2.5: The first three terms of a 17 i=1 (5i + 3) are ______________, ____...
 11.2.6: In Exercises 16, find the common difference for each arithmetic seq...
 11.2.7: In Exercises 716, write the first six terms of each arithmetic sequ...
 11.2.8: In Exercises 716, write the first six terms of each arithmetic sequ...
 11.2.9: In Exercises 716, write the first six terms of each arithmetic sequ...
 11.2.10: In Exercises 716, write the first six terms of each arithmetic sequ...
 11.2.11: In Exercises 716, write the first six terms of each arithmetic sequ...
 11.2.12: In Exercises 716, write the first six terms of each arithmetic sequ...
 11.2.13: In Exercises 716, write the first six terms of each arithmetic sequ...
 11.2.14: In Exercises 716, write the first six terms of each arithmetic sequ...
 11.2.15: In Exercises 716, write the first six terms of each arithmetic sequ...
 11.2.16: In Exercises 716, write the first six terms of each arithmetic sequ...
 11.2.17: In Exercises 1724, use the formula for the general term (the nth te...
 11.2.18: In Exercises 1724, use the formula for the general term (the nth te...
 11.2.19: In Exercises 1724, use the formula for the general term (the nth te...
 11.2.20: In Exercises 1724, use the formula for the general term (the nth te...
 11.2.21: In Exercises 1724, use the formula for the general term (the nth te...
 11.2.22: In Exercises 1724, use the formula for the general term (the nth te...
 11.2.23: In Exercises 1724, use the formula for the general term (the nth te...
 11.2.24: In Exercises 1724, use the formula for the general term (the nth te...
 11.2.25: In Exercises 2534, write a formula for the general term (the nth te...
 11.2.26: In Exercises 2534, write a formula for the general term (the nth te...
 11.2.27: In Exercises 2534, write a formula for the general term (the nth te...
 11.2.28: In Exercises 2534, write a formula for the general term (the nth te...
 11.2.29: In Exercises 2534, write a formula for the general term (the nth te...
 11.2.30: In Exercises 2534, write a formula for the general term (the nth te...
 11.2.31: In Exercises 2534, write a formula for the general term (the nth te...
 11.2.32: In Exercises 2534, write a formula for the general term (the nth te...
 11.2.33: In Exercises 2534, write a formula for the general term (the nth te...
 11.2.34: In Exercises 2534, write a formula for the general term (the nth te...
 11.2.35: Find the sum of the first 20 terms of the arithmetic sequence: 4, 1...
 11.2.36: Find the sum of the first 25 terms of the arithmetic sequence: 7, 1...
 11.2.37: Find the sum of the first 50 terms of the arithmetic sequence: 10,...
 11.2.38: Find the sum of the first 50 terms of the arithmetic sequence: 15,...
 11.2.39: Find 1 + 2 + 3 + 4 + g + 100, the sum of the first 100 natural numb...
 11.2.40: Find 2 + 4 + 6 + 8 + g + 200, the sum of the first 100 positive eve...
 11.2.41: Find the sum of the first 60 positive even integers.
 11.2.42: Find the sum of the first 80 positive even integers.
 11.2.43: Find the sum of the even integers between 21 and 45.
 11.2.44: Find the sum of the odd integers between 30 and 54.
 11.2.45: For Exercises 4550, write out the first three terms and the last te...
 11.2.46: For Exercises 4550, write out the first three terms and the last te...
 11.2.47: For Exercises 4550, write out the first three terms and the last te...
 11.2.48: For Exercises 4550, write out the first three terms and the last te...
 11.2.49: For Exercises 4550, write out the first three terms and the last te...
 11.2.50: For Exercises 4550, write out the first three terms and the last te...
 11.2.51: Use the graphs of the arithmetic sequences {an} and {bn} to solve E...
 11.2.52: Use the graphs of the arithmetic sequences {an} and {bn} to solve E...
 11.2.53: Use the graphs of the arithmetic sequences {an} and {bn} to solve E...
 11.2.54: Use the graphs of the arithmetic sequences {an} and {bn} to solve E...
 11.2.55: Use the graphs of the arithmetic sequences {an} and {bn} to solve E...
 11.2.56: Use the graphs of the arithmetic sequences {an} and {bn} to solve E...
 11.2.57: Use the graphs of the arithmetic sequences {an} and {bn} to solve E...
 11.2.58: Use the graphs of the arithmetic sequences {an} and {bn} to solve E...
 11.2.59: Use a system of two equations in two variables, a1 and d, to solve ...
 11.2.60: Use a system of two equations in two variables, a1 and d, to solve ...
 11.2.61: In 1970, 11.0% of Americans ages 25 and older had completed four ye...
 11.2.62: In 1970, 55.2% of Americans ages 25 and older had completed four ye...
 11.2.63: Company A pays $24,000 yearly with raises of $1600 per year. Compan...
 11.2.64: Company A pays $23,000 yearly with raises of $1200 per year. Compan...
 11.2.65: In Exercises 6566, we revisit the data from Chapter 1 showing the a...
 11.2.66: In Exercises 6566, we revisit the data from Chapter 1 showing the a...
 11.2.67: Use one of the models in Exercises 6566 and the formula for Sn to f...
 11.2.68: A company offers a starting yearly salary of $33,000 with raises of...
 11.2.69: You are considering two job offers. Company A will start you at $19...
 11.2.70: A theater has 30 seats in the first row, 32 seats in the second row...
 11.2.71: A section in a stadium has 20 seats in the first row, 23 seats in t...
 11.2.72: What is an arithmetic sequence? Give an example with your explanation.
 11.2.73: What is the common difference in an arithmetic sequence?
 11.2.74: Explain how to find the general term of an arithmetic sequence.
 11.2.75: Explain how to find the sum of the first n terms of an arithmetic s...
 11.2.76: Use the SEQ (sequence) capability of a graphing utility and the for...
 11.2.77: Use the capability of a graphing utility to calculate the sum of a ...
 11.2.78: Make Sense? In Exercises 7881, determine whether each statement mak...
 11.2.79: Make Sense? In Exercises 7881, determine whether each statement mak...
 11.2.80: Make Sense? In Exercises 7881, determine whether each statement mak...
 11.2.81: Make Sense? In Exercises 7881, determine whether each statement mak...
 11.2.82: In Exercises 8285, determine whether each statement is true or fals...
 11.2.83: In Exercises 8285, determine whether each statement is true or fals...
 11.2.84: In Exercises 8285, determine whether each statement is true or fals...
 11.2.85: In Exercises 8285, determine whether each statement is true or fals...
 11.2.86: Give examples of two different arithmetic sequences whose fourth te...
 11.2.87: In the sequence 21,700, 23,172, 24,644, 26,116,c, which term is 314...
 11.2.88: A degreeday is a unit used to measure the fuel requirements of bui...
 11.2.89: Show that the sum of the first n positive odd integers, 1 + 3 + 5 +...
 11.2.90: Solve: log(x2  25)  log(x + 5) = 3. (Section 9.5, Example 5)
 11.2.91: Solve: x2 + 3x 10. (Section 8.5, Example 1)
 11.2.92: Solve for P: A = Pt P + t . (Section 6.7, Example 1)
 11.2.93: Exercises 9395 will help you prepare for the material covered in th...
 11.2.94: Exercises 9395 will help you prepare for the material covered in th...
 11.2.95: Exercises 9395 will help you prepare for the material covered in th...
Solutions for Chapter 11.2: Arithmetic Sequences
Full solutions for Intermediate Algebra for College Students  6th Edition
ISBN: 9780321758934
Solutions for Chapter 11.2: Arithmetic Sequences
Get Full SolutionsSince 95 problems in chapter 11.2: Arithmetic Sequences have been answered, more than 9728 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. Chapter 11.2: Arithmetic Sequences includes 95 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. Intermediate Algebra for College Students was written by and is associated to the ISBN: 9780321758934.

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.

Diagonalization
A = S1 AS. A = eigenvalue matrix and S = eigenvector matrix of A. A must have n independent eigenvectors to make S invertible. All Ak = SA k SI.

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.

Fourier matrix F.
Entries Fjk = e21Cijk/n give orthogonal columns FT F = nI. Then y = Fe is the (inverse) Discrete Fourier Transform Y j = L cke21Cijk/n.

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

Hankel matrix H.
Constant along each antidiagonal; hij depends on i + j.

Hessenberg matrix H.
Triangular matrix with one extra nonzero adjacent diagonal.

Independent vectors VI, .. " vk.
No combination cl VI + ... + qVk = zero vector unless all ci = O. If the v's are the columns of A, the only solution to Ax = 0 is x = o.

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.

Normal equation AT Ax = ATb.
Gives the least squares solution to Ax = b if A has full rank n (independent columns). The equation says that (columns of A)·(b  Ax) = o.

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

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

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

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.

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.

Triangle inequality II u + v II < II u II + II v II.
For matrix norms II A + B II < II A II + II B II·

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

Vandermonde matrix V.
V c = b gives coefficients of p(x) = Co + ... + Cn_IXn 1 with P(Xi) = bi. Vij = (Xi)jI and det V = product of (Xk  Xi) for k > i.

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