 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 29916 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.

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!

CayleyHamilton Theorem.
peA) = det(A  AI) has peA) = zero matrix.

Change of basis matrix M.
The old basis vectors v j are combinations L mij Wi of the new basis vectors. The coordinates of CI VI + ... + cnvn = dl wI + ... + dn Wn are related by d = M c. (For n = 2 set VI = mll WI +m21 W2, V2 = m12WI +m22w2.)

Characteristic equation det(A  AI) = O.
The n roots are the eigenvalues of A.

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

Distributive Law
A(B + C) = AB + AC. Add then multiply, or mUltiply then add.

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.

Graph G.
Set of n nodes connected pairwise by m edges. A complete graph has all n(n  1)/2 edges between nodes. A tree has only n  1 edges and no closed loops.

Incidence matrix of a directed graph.
The m by n edgenode incidence matrix has a row for each edge (node i to node j), with entries 1 and 1 in columns i and j .

Left inverse A+.
If A has full column rank n, then A+ = (AT A)I AT has A+ A = In.

Linearly dependent VI, ... , Vn.
A combination other than all Ci = 0 gives L Ci Vi = O.

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.

Orthonormal vectors q 1 , ... , q n·
Dot products are q T q j = 0 if i =1= j and q T q i = 1. The matrix Q with these orthonormal columns has Q T Q = I. If m = n then Q T = Q 1 and q 1 ' ... , q n is an orthonormal basis for Rn : every v = L (v T q j )q j •

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).

Reduced row echelon form R = rref(A).
Pivots = 1; zeros above and below pivots; the r nonzero rows of R give a basis for the row space of A.

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.

Special solutions to As = O.
One free variable is Si = 1, other free variables = o.

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.

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

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