- 8.2.1: Find the first term and the common difference. 3, 8, 13, 18, c
- 8.2.2: Find the first term and the common difference. $1.08, $1.16, $1.24,...
- 8.2.3: Find the first term and the common difference. 9, 5, 1, -3, c
- 8.2.4: Find the first term and the common difference. -8, -5, -2, 1, 4, c
- 8.2.5: Find the first term and the common difference. 32, 94, 3, 154 ,
- 8.2.6: Find the first term and the common difference. 35, 110, -25, c
- 8.2.7: Find the first term and the common difference. $316, $313, $310, $3...
- 8.2.8: Find the 11th term of the arithmetic sequence0.07, 0.12, 0.17, c.
- 8.2.9: Find the 12th term of the arithmetic sequence2, 6, 10, c.
- 8.2.10: Find the 17th term of the arithmetic sequence7, 4, 1, c.
- 8.2.11: Find the 14th term of the arithmetic sequence3, 73, 53, c.
- 8.2.12: Find the 13th term of the arithmetic sequence$1200, $964.32, $728.6...
- 8.2.13: Find the 10th term of the arithmetic sequence$2345.78, $2967.54, $3...
- 8.2.14: In the sequence of Exercise 8, what term is thenumber 1.67?
- 8.2.15: In the sequence of Exercise 9, what term is thenumber 106?
- 8.2.16: In the sequence of Exercise 10, what term is -296?
- 8.2.17: In the sequence of Exercise 11, what term is -27?
- 8.2.18: Find a20 when a1 = 14 and d = -3.
- 8.2.19: Find a1 when d = 4 and a8 = 33.
- 8.2.20: Find d when a1 = 8 and a11 = 26.
- 8.2.21: Find n when a1 = 25, d = -14, and an = -507.
- 8.2.22: In an arithmetic sequence, a17 = -40 anda28 = -73. Find a1 and d. W...
- 8.2.23: In an arithmetic sequence, a17 = 253 anda32 = 956 . Find a1 and d. ...
- 8.2.24: Find the sum of the first 14 terms of the series11 + 7 + 3 + g.
- 8.2.25: Find the sum of the first 20 terms of the series5 + 8 + 11 + 14 + g
- 8.2.26: Find the sum of the first 300 natural numbers.
- 8.2.27: Find the sum of the first 400 even natural numbers.
- 8.2.28: Find the sum of the odd numbers 1 to 199,inclusive.
- 8.2.29: Find the sum of the multiples of 7 from 7 to 98,inclusive.
- 8.2.30: Find the sum of all multiples of 4 that arebetween 14 and 523.
- 8.2.31: If an arithmetic series has a1 = 2, d = 5, andn = 20, what is Sn?
- 8.2.32: If an arithmetic series has a1 = 7, d = -3, andn = 32, what is Sn?
- 8.2.33: Find the sum. a40k=112k + 32
- 8.2.34: Find the sum. 20k=58k
- 8.2.35: Find the sum. 19k=0k - 34
- 8.2.36: Find the sum. 50k=212000 - 3k2
- 8.2.37: Find the sum. 57k=127 - 4k13
- 8.2.38: Find the sum. 200k=10111.14k - 2.82 - a5k=1ak + 410b
- 8.2.39: Stacking Poles. How many poles will be in a stackof telephone poles...
- 8.2.40: Investment Return. Max, an investment counselor,sets up an investme...
- 8.2.41: Investment Return. Max, an investment counselor,sets up an investme...
- 8.2.42: Total Savings. If 10 is saved on October 1, 20 issaved on October 2...
- 8.2.43: Parachutist Free Fall. When a parachutist jumpsfrom an airplane, th...
- 8.2.44: Is this sequence arithmetic? What is the commondifference? What is ...
- 8.2.45: Band Formation. A formation of a marchingband has 10 marchers in th...
- 8.2.46: Garden Plantings. A gardener is making aplanting in the shape of a ...
- 8.2.47: Raw Material Production. In a manufacturingprocess, it took 3 units...
- 8.2.48: Solve. 7x - 2y = 4,x + 3y = 17
- 8.2.49: Solve. 2x + y + 3z = 12,x - 3y + 2z = 11,5x + 2y - 4z = -4
- 8.2.50: Find the vertices and the foci of the ellipse withequation 9x2 + 16...
- 8.2.51: Find an equation of the ellipse with vertices10, -52 and 10, 52 and...
- 8.2.52: Straight-Line Depreciation. A company buys anoffice machine for $52...
- 8.2.53: Find a formula for the sum of the first n oddnatural numbers:1 + 3 ...
- 8.2.54: Find three numbers in an arithmetic sequencesuch that the sum of th...
- 8.2.55: Find the first term and the common differencefor the arithmetic seq...
- 8.2.56: Insert three arithmetic means between -3 and 5.
- 8.2.57: Insert four arithmetic means between 4 and 13.
Solutions for Chapter 8.2: Arithmetic Sequences and Series
Full solutions for College Algebra: Graphs and Models | 5th Edition
Tv = Av + Vo = linear transformation plus shift.
Remove row i and column j; multiply the determinant by (-I)i + j •
Column picture of Ax = b.
The vector b becomes a combination of the columns of A. The system is solvable only when b is in the column space C (A).
Dot product = Inner product x T y = XI Y 1 + ... + Xn Yn.
Complex dot product is x T Y . Perpendicular vectors have x T y = O. (AB)ij = (row i of A)T(column j of B).
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 IIA-1 yll2 = Y T(AAT)-1 Y = 1 displayed by eigshow; axis lengths ad
Full row rank r = m.
Independent rows, at least one solution to Ax = b, column space is all of Rm. Full rank means full column rank or full row rank.
Invert A by row operations on [A I] to reach [I A-I].
Hessenberg matrix H.
Triangular matrix with one extra nonzero adjacent diagonal.
Hilbert matrix hilb(n).
Entries HU = 1/(i + j -1) = Jd X i- 1 xj-1dx. Positive definite but extremely small Amin and large condition number: H is ill-conditioned.
Hypercube matrix pl.
Row n + 1 counts corners, edges, faces, ... of a cube in Rn.
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.
A sequence of steps intended to approach the desired solution.
Current Law: net current (in minus out) is zero at each node. Voltage Law: Potential differences (voltage drops) add to zero around any closed loop.
Linear combination cv + d w or L C jV j.
Vector addition and scalar multiplication.
A directed graph that has constants Cl, ... , Cm associated with the edges.
IIA II. The ".e 2 norm" of A is the maximum ratio II Ax II/l1x II = O"max· Then II Ax II < IIAllllxll and IIABII < IIAIIIIBII and IIA + BII < IIAII + IIBII. Frobenius norm IIAII} = L La~. The.e 1 and.e oo norms are largest column and row sums of laij I.
Plane (or hyperplane) in Rn.
Vectors x with aT x = O. Plane is perpendicular to a =1= O.
Polar decomposition A = Q H.
Orthogonal Q times positive (semi)definite H.
Vector v in Rn.
Sequence of n real numbers v = (VI, ... , Vn) = point in Rn.
Volume of box.
The rows (or the columns) of A generate a box with volume I det(A) I.