 8.2.8.2.1: Fill in the blanks.A sequence is called an _______ sequence if the ...
 8.2.8.2.2: Fill in the blanks.The nth term of an arithmetic sequence has the f...
 8.2.8.2.3: Fill in the blanks.
 8.2.8.2.4: In Exercises 18, determine whether or not the sequence is arithmeti...
 8.2.8.2.5: In Exercises 18, determine whether or not the sequence is arithmeti...
 8.2.8.2.6: In Exercises 18, determine whether or not the sequence is arithmeti...
 8.2.8.2.7: In Exercises 18, determine whether or not the sequence is arithmeti...
 8.2.8.2.8: In Exercises 18, determine whether or not the sequence is arithmeti...
 8.2.8.2.9: In Exercises 916, write the first five terms of the sequence. Deter...
 8.2.8.2.10: In Exercises 916, write the first five terms of the sequence. Deter...
 8.2.8.2.11: In Exercises 916, write the first five terms of the sequence. Deter...
 8.2.8.2.12: In Exercises 916, write the first five terms of the sequence. Deter...
 8.2.8.2.13: In Exercises 916, write the first five terms of the sequence. Deter...
 8.2.8.2.14: In Exercises 916, write the first five terms of the sequence. Deter...
 8.2.8.2.15: In Exercises 916, write the first five terms of the sequence. Deter...
 8.2.8.2.16: In Exercises 916, write the first five terms of the sequence. Deter...
 8.2.8.2.17: In Exercises 1726, find a formula for for the arithmetic sequence.
 8.2.8.2.18: In Exercises 1726, find a formula for for the arithmetic sequence.
 8.2.8.2.19: In Exercises 1726, find a formula for for the arithmetic sequence.
 8.2.8.2.20: In Exercises 1726, find a formula for for the arithmetic sequence.
 8.2.8.2.21: In Exercises 1726, find a formula for for the arithmetic sequence.
 8.2.8.2.22: In Exercises 1726, find a formula for for the arithmetic sequence.
 8.2.8.2.23: In Exercises 1726, find a formula for for the arithmetic sequence.
 8.2.8.2.24: In Exercises 1726, find a formula for for the arithmetic sequence.
 8.2.8.2.25: In Exercises 1726, find a formula for for the arithmetic sequence.
 8.2.8.2.26: In Exercises 1726, find a formula for for the arithmetic sequence.
 8.2.8.2.27: In Exercises 2734, write the first five terms of the arithmetic seq...
 8.2.8.2.28: In Exercises 2734, write the first five terms of the arithmetic seq...
 8.2.8.2.29: In Exercises 2734, write the first five terms of the arithmetic seq...
 8.2.8.2.30: In Exercises 2734, write the first five terms of the arithmetic seq...
 8.2.8.2.31: In Exercises 2734, write the first five terms of the arithmetic seq...
 8.2.8.2.32: In Exercises 2734, write the first five terms of the arithmetic seq...
 8.2.8.2.33: In Exercises 2734, write the first five terms of the arithmetic seq...
 8.2.8.2.34: In Exercises 2734, write the first five terms of the arithmetic seq...
 8.2.8.2.35: In Exercises 3538, write the first five terms of the arithmetic seq...
 8.2.8.2.36: In Exercises 3538, write the first five terms of the arithmetic seq...
 8.2.8.2.37: In Exercises 3538, write the first five terms of the arithmetic seq...
 8.2.8.2.38: In Exercises 3538, write the first five terms of the arithmetic seq...
 8.2.8.2.39: In Exercises 39 42, the first two terms of the arithmetic sequence ...
 8.2.8.2.40: In Exercises 39 42, the first two terms of the arithmetic sequence ...
 8.2.8.2.41: In Exercises 39 42, the first two terms of the arithmetic sequence ...
 8.2.8.2.42: In Exercises 39 42, the first two terms of the arithmetic sequence ...
 8.2.8.2.43: In Exercises 43 46, use a graphing utility to graph the first 10 te...
 8.2.8.2.44: In Exercises 43 46, use a graphing utility to graph the first 10 te...
 8.2.8.2.45: In Exercises 43 46, use a graphing utility to graph the first 10 te...
 8.2.8.2.46: In Exercises 43 46, use a graphing utility to graph the first 10 te...
 8.2.8.2.47: In Exercises 4752, use the table feature of a graphing utility to f...
 8.2.8.2.48: In Exercises 4752, use the table feature of a graphing utility to f...
 8.2.8.2.49: In Exercises 4752, use the table feature of a graphing utility to f...
 8.2.8.2.50: In Exercises 4752, use the table feature of a graphing utility to f...
 8.2.8.2.51: In Exercises 4752, use the table feature of a graphing utility to f...
 8.2.8.2.52: In Exercises 4752, use the table feature of a graphing utility to f...
 8.2.8.2.53: In Exercises 5360, find the sum of the finite arithmetic sequence.
 8.2.8.2.54: In Exercises 5360, find the sum of the finite arithmetic sequence.
 8.2.8.2.55: In Exercises 5360, find the sum of the finite arithmetic sequence.
 8.2.8.2.56: In Exercises 5360, find the sum of the finite arithmetic sequence.
 8.2.8.2.57: In Exercises 5360, find the sum of the finite arithmetic sequence.
 8.2.8.2.58: In Exercises 5360, find the sum of the finite arithmetic sequence.
 8.2.8.2.59: In Exercises 5360, find the sum of the finite arithmetic sequence.
 8.2.8.2.60: In Exercises 5360, find the sum of the finite arithmetic sequence.
 8.2.8.2.61: In Exercises 61 66, find the indicated th partial sum of the arithm...
 8.2.8.2.62: In Exercises 61 66, find the indicated th partial sum of the arithm...
 8.2.8.2.63: In Exercises 61 66, find the indicated th partial sum of the arithm...
 8.2.8.2.64: In Exercises 61 66, find the indicated th partial sum of the arithm...
 8.2.8.2.65: In Exercises 61 66, find the indicated th partial sum of the arithm...
 8.2.8.2.66: In Exercises 61 66, find the indicated th partial sum of the arithm...
 8.2.8.2.67: In Exercises 6774, find the partial sum without using a graphing ut...
 8.2.8.2.68: In Exercises 6774, find the partial sum without using a graphing ut...
 8.2.8.2.69: In Exercises 6774, find the partial sum without using a graphing ut...
 8.2.8.2.70: In Exercises 6774, find the partial sum without using a graphing ut...
 8.2.8.2.71: In Exercises 6774, find the partial sum without using a graphing ut...
 8.2.8.2.72: In Exercises 6774, find the partial sum without using a graphing ut...
 8.2.8.2.73: In Exercises 6774, find the partial sum without using a graphing ut...
 8.2.8.2.74: In Exercises 6774, find the partial sum without using a graphing ut...
 8.2.8.2.75: In Exercises 7580, use a graphing utility to find the partial sum.
 8.2.8.2.76: In Exercises 7580, use a graphing utility to find the partial sum.
 8.2.8.2.77: In Exercises 7580, use a graphing utility to find the partial sum.
 8.2.8.2.78: In Exercises 7580, use a graphing utility to find the partial sum.
 8.2.8.2.79: In Exercises 7580, use a graphing utility to find the partial sum.
 8.2.8.2.80: In Exercises 7580, use a graphing utility to find the partial sum.
 8.2.8.2.81: Brick Pattern A brick patio has the approximate shape of a trapezoi...
 8.2.8.2.82: Number of Logs Logs are stacked in a pile, as shown in the figure. ...
 8.2.8.2.83: Sales A small hardware store makes a profit of $20,000 during its f...
 8.2.8.2.84: Falling Object An object with negligible air resistance is dropped ...
 8.2.8.2.85: Sales The table shows the sales (in billions of dollars) for CocaC...
 8.2.8.2.86: Education The table shows the numbers (in thousands) of masters deg...
 8.2.8.2.87: True or False? In Exercises 87 and 88, determine whether the statem...
 8.2.8.2.88: True or False? In Exercises 87 and 88, determine whether the statem...
 8.2.8.2.89: In Exercises 89 and 90, find the first 10 terms of the sequence.
 8.2.8.2.90: In Exercises 89 and 90, find the first 10 terms of the sequence.
 8.2.8.2.91: Think About It The sum of the first 20 terms of an arithmetic seque...
 8.2.8.2.92: Think About It The sum of the first n terms of an arithmetic sequen...
 8.2.8.2.93: Think About It Decide whether it is possible to fill in the blanks ...
 8.2.8.2.94: Gauss Carl Friedrich Gauss, a famous nineteenth century mathematici...
 8.2.8.2.95: In Exercises 9598, find the sum using the method from Exercise 94
 8.2.8.2.96: In Exercises 9598, find the sum using the method from Exercise 94
 8.2.8.2.97: In Exercises 9598, find the sum using the method from Exercise 94
 8.2.8.2.98: In Exercises 9598, find the sum using the method from Exercise 94
 8.2.8.2.99: In Exercises 99 and 100, use GaussJordan elimination to solve the ...
 8.2.8.2.100: In Exercises 99 and 100, use GaussJordan elimination to solve the ...
 8.2.8.2.101: In Exercises 101 and 102, use a determinant to find the area of the...
 8.2.8.2.102: In Exercises 101 and 102, use a determinant to find the area of the...
 8.2.8.2.103: Make a Decision To work an extended application analyzing the amoun...
Solutions for Chapter 8.2: Arithmetic Sequences and Partial Sums
Full solutions for Precalculus With Limits A Graphing Approach  5th Edition
ISBN: 9780618851522
Solutions for Chapter 8.2: Arithmetic Sequences and Partial Sums
Get Full SolutionsThis textbook survival guide was created for the textbook: Precalculus With Limits A Graphing Approach, edition: 5. Since 103 problems in chapter 8.2: Arithmetic Sequences and Partial Sums have been answered, more than 35926 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Precalculus With Limits A Graphing Approach was written by and is associated to the ISBN: 9780618851522. Chapter 8.2: Arithmetic Sequences and Partial Sums includes 103 full stepbystep solutions.

Affine transformation
Tv = Av + Vo = linear transformation plus shift.

Back substitution.
Upper triangular systems are solved in reverse order Xn to Xl.

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

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

Echelon matrix U.
The first nonzero entry (the pivot) in each row comes in a later column than the pivot in the previous row. All zero rows come last.

Eigenvalue A and eigenvector x.
Ax = AX with x#O so det(A  AI) = o.

Ellipse (or ellipsoid) x T Ax = 1.
A must be positive definite; the axes of the ellipse are eigenvectors of A, with lengths 1/.JI. (For IIx II = 1 the vectors y = Ax lie on the ellipse IIA1 yll2 = Y T(AAT)1 Y = 1 displayed by eigshow; axis lengths ad

Fast Fourier Transform (FFT).
A factorization of the Fourier matrix Fn into e = log2 n matrices Si times a permutation. Each Si needs only nl2 multiplications, so Fnx and Fn1c can be computed with ne/2 multiplications. Revolutionary.

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.

lAII = l/lAI and IATI = IAI.
The big formula for det(A) has a sum of n! terms, the cofactor formula uses determinants of size n  1, volume of box = I det( A) I.

Least squares solution X.
The vector x that minimizes the error lie 112 solves AT Ax = ATb. Then e = b  Ax is orthogonal to all columns of A.

Left nullspace N (AT).
Nullspace of AT = "left nullspace" of A because y T A = OT.

Orthogonal matrix Q.
Square matrix with orthonormal columns, so QT = Ql. Preserves length and angles, IIQxll = IIxll and (QX)T(Qy) = xTy. AlllAI = 1, with orthogonal eigenvectors. Examples: Rotation, reflection, permutation.

Projection p = a(aTblaTa) onto the line through a.
P = aaT laTa has rank l.

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.

Rayleigh quotient q (x) = X T Ax I x T x for symmetric A: Amin < q (x) < Amax.
Those extremes are reached at the eigenvectors x for Amin(A) and Amax(A).

Schur complement S, D  C A } B.
Appears in block elimination on [~ g ].

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