 9.1.1: An ________ ________ is a function whose domain is the set of posit...
 9.1.2: A sequence is a ________ sequence when the domain of the function c...
 9.1.3: If you are given one or more of the first few terms of a sequence, ...
 9.1.4: If is a positive integer, then ________ is defined as n! 1 2 3 4 . ...
 9.1.5: For the sum is called the ________ of summation, is the ________ li...
 9.1.6: The sum of the terms of a finite or infinite sequence is called a _...
 9.1.7: an 4n 7
 9.1.8: an 2 1 3n a
 9.1.9: an 2n an
 9.1.10: an 1 2 n an
 9.1.11: an n n 2 a
 9.1.12: an 6n 3n2 1 a
 9.1.13: an 1 1n n an
 9.1.14: an 1n n2 an
 9.1.15: an 2n 3n
 9.1.16: an 1 n32 a
 9.1.17: an 2 3
 9.1.18: an 1 1n an
 9.1.19: a 2 6 n nn 1n 2 an 1
 9.1.20: an nn a 2 6 n n
 9.1.21: an 1n n n 1 an
 9.1.22: an 1n1 n2 1 an
 9.1.23: a nn 1 n 1n3n 2 an 1
 9.1.24: an 1n1 a nn 1 n 1
 9.1.25: an 4n 2n2 3
 9.1.26: an 4n2 n 3 nn 1n 2 an 4n
 9.1.27: an 2 3 n n
 9.1.28: an 2 4 n a
 9.1.29: an 160.5n1 an
 9.1.30: an 80.75n1 an
 9.1.31: an 2n n 1 a
 9.1.32: an 3n2 n2 1 an
 9.1.33: an 8 n 1 2
 9.1.34: an 8n n 1 an
 9.1.35: an 40.5n1 an
 9.1.36: an 4n n! a
 9.1.37: 3, 7, 11, 15, 19, . . .
 9.1.38: 0, 3, 8, 15, 24, . . .
 9.1.39: , . . . 2 3, 3 4, 4 5, 5 6, 6 7, . . .
 9.1.40: 1 2, 1 4, 1 8, 1 16 , . . .
 9.1.41: 2 1, 3 3, 4 5, 5 7, 6 9, . . .
 9.1.42: 1 3, 2 9, 4 27, 8 81, . . .
 9.1.43: 1, , . . . 1 4, 1 9, 1 16, 1 25, . . .
 9.1.44: 1, 1 2, 1 6, 1 24, 1 120 1, , . . .
 9.1.45: 1, 1, 1, 1, 1, . . .
 9.1.46: 1, 3, 1, 3, 1, . . .
 9.1.47: 1, 3, 32 2 , 33 6 , 34 24, 35 120, . . .
 9.1.48: 1 1 2, 1 3 4, 1 7 8, 1 15 16, 1 31 32, . . . 1, 3,
 9.1.49: a k 4 1 28,
 9.1.50: a k 1 1 3,
 9.1.51: a0 1, a1 2, ak ak2 1 2ak1 ak1
 9.1.52: a0 1, a1 1, ak ak2 ak1 a0
 9.1.53: a1 6, ak1 ak 2 n n
 9.1.54: a1 25, ak1 ak 5 a1
 9.1.55: a1 81, 3ak
 9.1.56: a1 14, ak1 2ak ak1
 9.1.57: Write the first 12 terms of the Fibonacci sequence and the first 10...
 9.1.58: Using the definition for in Exercise 57, show that can be defined r...
 9.1.59: an 5 n!
 9.1.60: an n! 2n 1 an
 9.1.61: an 1 n 1! an
 9.1.62: an 12n1 2n 1! an 1 n
 9.1.63: 4! 6!
 9.1.64: 12! 4! 8!
 9.1.65: n 1! n! 12
 9.1.66: 2n 1! 2n 1! n 1
 9.1.67: 5 i1 2i 1 2n
 9.1.68: 5 j3 1 j 2 3 5
 9.1.69: 4 k1 10
 9.1.70: 4 i0 i 2
 9.1.71: 5 k2 k 12k 3 4
 9.1.72: 4 i1 i 12 i 13 5 k2
 9.1.73: 4 i1 2i
 9.1.74: 4 j0 2j
 9.1.75: 5 n0 1 2n 1
 9.1.76: 4 k0 1k k 1 5
 9.1.77: 4 k0 1k k!
 9.1.78: 25 n0 1 4 n
 9.1.79: 1 31 1 32 1 33 . . . 1 39 25 n0
 9.1.80: 5 1 1 5 1 2 5 1 3 . . . 5 1 15 1 31
 9.1.81: 2 1 8 3 22 8 3 . . . 2 8 8 3 5 1 1
 9.1.82: 1 1 6 2 1 2 6 2 . . . 1 6 6 2 2 1 8
 9.1.83: 3 9 27 81 243 729
 9.1.84: 1 1 2 1 4 1 8 . . . 1 128 3
 9.1.85: 1 12 1 22 1 32 1 42 . . . 1 202 1
 9.1.86: 1 1 3 1 2 4 1 3 5 . . . 1 10 12 1
 9.1.87: 1 4 3 8 7 16 15 32 31 64 1
 9.1.88: 1 2 2 4 6 8 24 16 120 32 720 64 1 4
 9.1.89: i1 5 1 2 i 1
 9.1.90: i1 2 1 3 i
 9.1.91: n1 41 2 n
 9.1.92: n1 81 4 n
 9.1.93: i1 6 10i
 9.1.94: k1 1 10 k
 9.1.95: k1 7 1 10 k
 9.1.96: i1 2 10 i
 9.1.97: Compound Interest An investor deposits $10,000 in an account that e...
 9.1.98: AIDS Cases The numbers (in thousands) of AIDS cases reportedfrom 20...
 9.1.99: 4 i1 i 2 2i 4 i1 i 2 2 4 i1 i An 10,
 9.1.100: 4 j1 2 j 6 j3 2 j2
 9.1.101: Find the arithmetic mean of the six checking account balances $327....
 9.1.102: Proof Prove that ni1xi x 0.x 1
 9.1.103: Proof Prove that ni1xi x2 ni1x 2i 1nni1xi2.n
 9.1.104: HOW DO YOU SEE IT? The graph represents the first 10 terms of a seq...
 9.1.105: an xn n!
 9.1.106: an 1n x2n1 2n 1 an
 9.1.107: Cube A cube is made up of 27 unit cubes (a unit cube has a length, ...
Solutions for Chapter 9.1: Sequences and Series
Full solutions for Precalculus with Limits  3rd Edition
ISBN: 9781133947202
Solutions for Chapter 9.1: Sequences and Series
Get Full SolutionsSince 107 problems in chapter 9.1: Sequences and Series have been answered, more than 36337 students have viewed full stepbystep solutions from this chapter. Chapter 9.1: Sequences and Series includes 107 full stepbystep solutions. Precalculus with Limits was written by and is associated to the ISBN: 9781133947202. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Precalculus with Limits, edition: 3.

Compounded k times per year
Interest compounded using the formula A = Pa1 + rkbkt where k = 1 is compounded annually, k = 4 is compounded quarterly k = 12 is compounded monthly, etc.

Divergence
A sequence or series diverges if it does not converge

Division algorithm for polynomials
Given ƒ(x), d(x) ? 0 there are unique polynomials q1x (quotient) and r1x(remainder) ƒ1x2 = d1x2q1x2 + r1x2 with with either r1x2 = 0 or degree of r(x) 6 degree of d1x2

Dot product
The number found when the corresponding components of two vectors are multiplied and then summed

Equivalent arrows
Arrows that have the same magnitude and direction.

Equivalent systems of equations
Systems of equations that have the same solution.

Extracting square roots
A method for solving equations in the form x 2 = k.

Finite sequence
A function whose domain is the first n positive integers for some fixed integer n.

Logarithm
An expression of the form logb x (see Logarithmic function)

Logarithmic form
An equation written with logarithms instead of exponents

Minor axis
The perpendicular bisector of the major axis of an ellipse with endpoints on the ellipse.

Multiplication property of equality
If u = v and w = z, then uw = vz

Negative numbers
Real numbers shown to the left of the origin on a number line.

Numerical derivative of ƒ at a
NDER f(a) = ƒ1a + 0.0012  ƒ1a  0.00120.002

Octants
The eight regions of space determined by the coordinate planes.

Product of complex numbers
(a + bi)(c + di) = (ac  bd) + (ad + bc)i

Rose curve
A graph of a polar equation or r = a cos nu.

Slant asymptote
An end behavior asymptote that is a slant line

Standard form: equation of a circle
(x  h)2 + (y  k2) = r 2

Trigonometric form of a complex number
r(cos ? + i sin ?)