 8.2.1: Fill in each blank so that the resulting statement is true. A seque...
 8.2.2: Fill in each blank so that the resulting statement is true. The nth...
 8.2.3: Fill in each blank so that the resulting statement is true. The sum...
 8.2.4: Fill in each blank so that the resulting statement is true. The fir...
 8.2.5: Fill in each blank so that the resulting statement is true. The fir...
 8.2.6: In Exercises 114, write the first six terms of each arithmetic sequ...
 8.2.7: In Exercises 114, write the first six terms of each arithmetic sequ...
 8.2.8: In Exercises 114, write the first six terms of each arithmetic sequ...
 8.2.9: In Exercises 114, write the first six terms of each arithmetic sequ...
 8.2.10: In Exercises 114, write the first six terms of each arithmetic sequ...
 8.2.11: In Exercises 114, write the first six terms of each arithmetic sequ...
 8.2.12: In Exercises 114, write the first six terms of each arithmetic sequ...
 8.2.13: In Exercises 114, write the first six terms of each arithmetic sequ...
 8.2.14: In Exercises 114, write the first six terms of each arithmetic sequ...
 8.2.15: In Exercises 1522, find the indicated term of the arithmetic sequen...
 8.2.16: In Exercises 1522, find the indicated term of the arithmetic sequen...
 8.2.17: In Exercises 1522, find the indicated term of the arithmetic sequen...
 8.2.18: In Exercises 1522, find the indicated term of the arithmetic sequen...
 8.2.19: In Exercises 1522, find the indicated term of the arithmetic sequen...
 8.2.20: In Exercises 1522, find the indicated term of the arithmetic sequen...
 8.2.21: In Exercises 1522, find the indicated term of the arithmetic sequen...
 8.2.22: In Exercises 1522, find the indicated term of the arithmetic sequen...
 8.2.23: In Exercises 2334, write a formula for the general term (the nth te...
 8.2.24: In Exercises 2334, write a formula for the general term (the nth te...
 8.2.25: In Exercises 2334, write a formula for the general term (the nth te...
 8.2.26: In Exercises 2334, write a formula for the general term (the nth te...
 8.2.27: In Exercises 2334, write a formula for the general term (the nth te...
 8.2.28: In Exercises 2334, write a formula for the general term (the nth te...
 8.2.29: In Exercises 2334, write a formula for the general term (the nth te...
 8.2.30: In Exercises 2334, write a formula for the general term (the nth te...
 8.2.31: In Exercises 2334, write a formula for the general term (the nth te...
 8.2.32: In Exercises 2334, write a formula for the general term (the nth te...
 8.2.33: In Exercises 2334, write a formula for the general term (the nth te...
 8.2.34: In Exercises 2334, write a formula for the general term (the nth te...
 8.2.35: Find the sum of the first 20 terms of the arithmetic sequence: 4, 1...
 8.2.36: Find the sum of the first 25 terms of the arithmetic sequence: 7, 1...
 8.2.37: Find the sum of the first 50 terms of the arithmetic sequence: 10,...
 8.2.38: Find the sum of the first 50 terms of the arithmetic sequence: 15,...
 8.2.39: Find 1 + 2 + 3 + 4 + g+ 100, the sum of the first 100 natural numbers.
 8.2.40: Find 2 + 4 + 6 + 8 + g+ 200, the sum of the first 100 positive even...
 8.2.41: Find the sum of the first 60 positive even integers.
 8.2.42: Find the sum of the first 80 positive even integers.
 8.2.43: Find the sum of the even integers between 21 and 45.
 8.2.44: Find the sum of the odd integers between 30 and 54.
 8.2.45: For Exercises 4550, write out the first three terms and the last te...
 8.2.46: For Exercises 4550, write out the first three terms and the last te...
 8.2.47: For Exercises 4550, write out the first three terms and the last te...
 8.2.48: For Exercises 4550, write out the first three terms and the last te...
 8.2.49: For Exercises 4550, write out the first three terms and the last te...
 8.2.50: For Exercises 4550, write out the first three terms and the last te...
 8.2.51: Use the graphs of the arithmetic sequences {an} and {bn} to solve E...
 8.2.52: Use the graphs of the arithmetic sequences {an} and {bn} to solve E...
 8.2.53: Use the graphs of the arithmetic sequences {an} and {bn} to solve E...
 8.2.54: Use the graphs of the arithmetic sequences {an} and {bn} to solve E...
 8.2.55: Use the graphs of the arithmetic sequences {an} and {bn} to solve E...
 8.2.56: Use the graphs of the arithmetic sequences {an} and {bn} to solve E...
 8.2.57: Use the graphs of the arithmetic sequences {an} and {bn} to solve E...
 8.2.58: Use the graphs of the arithmetic sequences {an} and {bn} to solve E...
 8.2.59: Use a system of two equations in two variables, a1 and d, to solve ...
 8.2.60: Use a system of two equations in two variables, a1 and d, to solve ...
 8.2.61: The bar graph shows changes in the percentage of college graduates ...
 8.2.62: The bar graph shows changes in the percentage of college graduates ...
 8.2.63: Company A pays $24,000 yearly with raises of $1600 per year. Compan...
 8.2.64: Company A pays $23,000 yearly with raises of $1200 per year. Compan...
 8.2.65: The bar graph shows the average dormitory charges at public and pri...
 8.2.66: The bar graph shows the average dormitory charges at public and pri...
 8.2.67: Use one of the models in Exercises 6566 and the formula for Sn to f...
 8.2.68: A company offers a starting yearly salary of $33,000 with raises of...
 8.2.69: You are considering two job offers. Company A will start you at $19...
 8.2.70: A theater has 30 seats in the first row, 32 seats in the second row...
 8.2.71: A section in a stadium has 20 seats in the first row, 23 seats in t...
 8.2.72: What is an arithmetic sequence? Give an example with your explanation.
 8.2.73: What is the common difference in an arithmetic sequence?
 8.2.74: Explain how to find the general term of an arithmetic sequence.
 8.2.75: Explain how to find the sum of the first n terms of an arithmetic s...
 8.2.76: Use the SEQ (sequence) capability of a graphing utility and the for...
 8.2.77: Use the capability of a graphing utility to calculate the sum of a ...
 8.2.78: In Exercises 7881, determine whether each statement makes sense or ...
 8.2.79: In Exercises 7881, determine whether each statement makes sense or ...
 8.2.80: In Exercises 7881, determine whether each statement makes sense or ...
 8.2.81: In Exercises 7881, determine whether each statement makes sense or ...
 8.2.82: In the sequence 21,700, 23,172, 24,644, 26,116, . . . ,which term i...
 8.2.83: A degreeday is a unit used to measure the fuel requirements of bui...
 8.2.84: Show that the sum of the first n positive odd integers, 1 + 3 + 5 +...
 8.2.85: Write an equation in pointslope form and slopeintercept form for ...
 8.2.86: Among all pairs of numbers whose sum is 24, find a pair whose produ...
 8.2.87: Solve: log2(x + 9)  log2 x = 1. (Section 4.4, Example 7)
 8.2.88: Exercises 8890 will help you prepare for the material covered in th...
 8.2.89: Exercises 8890 will help you prepare for the material covered in th...
 8.2.90: Exercises 8890 will help you prepare for the material covered in th...
Solutions for Chapter 8.2: Arithmetic Sequences
Full solutions for College Algebra  7th Edition
ISBN: 9780134469164
Solutions for Chapter 8.2: Arithmetic Sequences
Get Full SolutionsSince 90 problems in chapter 8.2: Arithmetic Sequences have been answered, more than 32547 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. College Algebra was written by and is associated to the ISBN: 9780134469164. Chapter 8.2: Arithmetic Sequences includes 90 full stepbystep solutions. This textbook survival guide was created for the textbook: College Algebra , edition: 7.

Adjacency matrix of a graph.
Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected). Adjacency matrix of a graph. Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected).

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.

Big formula for n by n determinants.
Det(A) is a sum of n! terms. For each term: Multiply one entry from each row and column of A: rows in order 1, ... , nand column order given by a permutation P. Each of the n! P 's has a + or  sign.

Cholesky factorization
A = CTC = (L.J]))(L.J]))T for positive definite A.

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

Companion matrix.
Put CI, ... ,Cn in row n and put n  1 ones just above the main diagonal. Then det(A  AI) = ±(CI + c2A + C3A 2 + .•. + cnA nl  An).

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.

Indefinite matrix.
A symmetric matrix with eigenvalues of both signs (+ and  ).

Length II x II.
Square root of x T x (Pythagoras in n dimensions).

Multiplicities AM and G M.
The algebraic multiplicity A M of A is the number of times A appears as a root of det(A  AI) = O. The geometric multiplicity GM is the number of independent eigenvectors for A (= dimension of the eigenspace).

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

Permutation matrix P.
There are n! orders of 1, ... , n. The n! P 's have the rows of I in those orders. P A puts the rows of A in the same order. P is even or odd (det P = 1 or 1) based on the number of row exchanges to reach I.

Pivot.
The diagonal entry (first nonzero) at the time when a row is used in elimination.

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

Rank r (A)
= number of pivots = dimension of column space = dimension of row space.

Solvable system Ax = b.
The right side b is in the column space of A.

Symmetric factorizations A = LDLT and A = QAQT.
Signs in A = signs in D.

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

Trace of A
= sum of diagonal entries = sum of eigenvalues of A. Tr AB = Tr BA.

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