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Intermediate Algebra

Chapter 12

Intermediate AlgebraChapter 12

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Table of contents
  1. Preface
  2. 1 Foundations
    1. Introduction
    2. 1.1 Use the Language of Algebra
    3. 1.2 Integers
    4. 1.3 Fractions
    5. 1.4 Decimals
    6. 1.5 Properties of Real Numbers
    7. Chapter Review
      1. Key Terms
      2. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  3. 2 Solving Linear Equations
    1. Introduction
    2. 2.1 Use a General Strategy to Solve Linear Equations
    3. 2.2 Use a Problem Solving Strategy
    4. 2.3 Solve a Formula for a Specific Variable
    5. 2.4 Solve Mixture and Uniform Motion Applications
    6. 2.5 Solve Linear Inequalities
    7. 2.6 Solve Compound Inequalities
    8. 2.7 Solve Absolute Value Inequalities
    9. Chapter Review
      1. Key Terms
      2. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  4. 3 Graphs and Functions
    1. Introduction
    2. 3.1 Graph Linear Equations in Two Variables
    3. 3.2 Slope of a Line
    4. 3.3 Find the Equation of a Line
    5. 3.4 Graph Linear Inequalities in Two Variables
    6. 3.5 Relations and Functions
    7. 3.6 Graphs of Functions
    8. Chapter Review
      1. Key Terms
      2. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  5. 4 Systems of Linear Equations
    1. Introduction
    2. 4.1 Solve Systems of Linear Equations with Two Variables
    3. 4.2 Solve Applications with Systems of Equations
    4. 4.3 Solve Mixture Applications with Systems of Equations
    5. 4.4 Solve Systems of Equations with Three Variables
    6. 4.5 Solve Systems of Equations Using Matrices
    7. 4.6 Solve Systems of Equations Using Determinants
    8. 4.7 Graphing Systems of Linear Inequalities
    9. Chapter Review
      1. Key Terms
      2. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  6. 5 Polynomials and Polynomial Functions
    1. Introduction
    2. 5.1 Add and Subtract Polynomials
    3. 5.2 Properties of Exponents and Scientific Notation
    4. 5.3 Multiply Polynomials
    5. 5.4 Dividing Polynomials
    6. Chapter Review
      1. Key Terms
      2. Key Concepts
    7. Exercises
      1. Review Exercises
      2. Practice Test
  7. 6 Factoring
    1. Introduction to Factoring
    2. 6.1 Greatest Common Factor and Factor by Grouping
    3. 6.2 Factor Trinomials
    4. 6.3 Factor Special Products
    5. 6.4 General Strategy for Factoring Polynomials
    6. 6.5 Polynomial Equations
    7. Chapter Review
      1. Key Terms
      2. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  8. 7 Rational Expressions and Functions
    1. Introduction
    2. 7.1 Multiply and Divide Rational Expressions
    3. 7.2 Add and Subtract Rational Expressions
    4. 7.3 Simplify Complex Rational Expressions
    5. 7.4 Solve Rational Equations
    6. 7.5 Solve Applications with Rational Equations
    7. 7.6 Solve Rational Inequalities
    8. Chapter Review
      1. Key Terms
      2. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  9. 8 Roots and Radicals
    1. Introduction
    2. 8.1 Simplify Expressions with Roots
    3. 8.2 Simplify Radical Expressions
    4. 8.3 Simplify Rational Exponents
    5. 8.4 Add, Subtract, and Multiply Radical Expressions
    6. 8.5 Divide Radical Expressions
    7. 8.6 Solve Radical Equations
    8. 8.7 Use Radicals in Functions
    9. 8.8 Use the Complex Number System
    10. Chapter Review
      1. Key Terms
      2. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  10. 9 Quadratic Equations and Functions
    1. Introduction
    2. 9.1 Solve Quadratic Equations Using the Square Root Property
    3. 9.2 Solve Quadratic Equations by Completing the Square
    4. 9.3 Solve Quadratic Equations Using the Quadratic Formula
    5. 9.4 Solve Quadratic Equations in Quadratic Form
    6. 9.5 Solve Applications of Quadratic Equations
    7. 9.6 Graph Quadratic Functions Using Properties
    8. 9.7 Graph Quadratic Functions Using Transformations
    9. 9.8 Solve Quadratic Inequalities
    10. Chapter Review
      1. Key Terms
      2. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  11. 10 Exponential and Logarithmic Functions
    1. Introduction
    2. 10.1 Finding Composite and Inverse Functions
    3. 10.2 Evaluate and Graph Exponential Functions
    4. 10.3 Evaluate and Graph Logarithmic Functions
    5. 10.4 Use the Properties of Logarithms
    6. 10.5 Solve Exponential and Logarithmic Equations
    7. Chapter Review
      1. Key Terms
      2. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  12. 11 Conics
    1. Introduction
    2. 11.1 Distance and Midpoint Formulas; Circles
    3. 11.2 Parabolas
    4. 11.3 Ellipses
    5. 11.4 Hyperbolas
    6. 11.5 Solve Systems of Nonlinear Equations
    7. Chapter Review
      1. Key Terms
      2. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  13. 12 Sequences, Series and Binomial Theorem
    1. Introduction
    2. 12.1 Sequences
    3. 12.2 Arithmetic Sequences
    4. 12.3 Geometric Sequences and Series
    5. 12.4 Binomial Theorem
    6. Chapter Review
      1. Key Terms
      2. Key Concepts
    7. Exercises
      1. Review Exercises
      2. Practice Test
  14. Answer Key
    1. Chapter 1
    2. Chapter 2
    3. Chapter 3
    4. Chapter 4
    5. Chapter 5
    6. Chapter 6
    7. Chapter 7
    8. Chapter 8
    9. Chapter 9
    10. Chapter 10
    11. Chapter 11
    12. Chapter 12
  15. Index

Try It

12.1

−1 , 2 , 5 , 8 , 11 −1 , 2 , 5 , 8 , 11

12.2

−3 , −1 , 1 , 3 , 5 −3 , −1 , 1 , 3 , 5

12.3

7 , 13 , 31 , 85 , 247 7 , 13 , 31 , 85 , 247

12.4

−3 , −1 , 3 , 11 , 27 −3 , −1 , 3 , 11 , 27

12.5

−1 , 4 , −9 , 16 , −25 −1 , 4 , −9 , 16 , −25

12.6

1 , −8 , 27 , −64 , 125 1 , −8 , 27 , −64 , 125

12.7

a n = 3 n a n = 3 n

12.8

a n = 5 n a n = 5 n

12.9

a n = ( −1 ) n 3 n a n = ( −1 ) n 3 n

12.10

a n = ( −1 ) n + 1 n 2 a n = ( −1 ) n + 1 n 2

12.11

a n = 1 2 n a n = 1 2 n

12.12

a n = 1 n 2 a n = 1 n 2

12.13

2 , 1 , 1 3 , 1 12 , 1 60 2 , 1 , 1 3 , 1 12 , 1 60

12.14

3 , 3 2 , 1 2 , 1 8 , 1 40 3 , 3 2 , 1 2 , 1 8 , 1 40

12.15

1 2 , 1 6 , 1 12 , 1 20 , 1 30 1 2 , 1 6 , 1 12 , 1 20 , 1 30

12.16

1 2 , 1 3 , 1 4 , 1 5 , 1 6 1 2 , 1 3 , 1 4 , 1 5 , 1 6

12.17

45

12.18

60

12.19

16 3 16 3

12.21

n = 1 5 1 2 n n = 1 5 1 2 n

12.22

n = 1 5 1 n 2 n = 1 5 1 n 2

12.23

n = 1 5 ( −1 ) n + 1 n 2 n = 1 5 ( −1 ) n + 1 n 2

12.24

n = 1 5 ( −1 ) n 2 n n = 1 5 ( −1 ) n 2 n

12.25

The sequence is arithmetic with common difference d=11d=11. The sequence is arithmetic with common difference d=−6d=−6.
The sequence is not arithmetic as all the differences between the consecutive terms are not the same.

12.26

The sequence is not arithmetic as all the differences between the consecutive terms are not the same. The sequence is arithmetic with common difference d=2.d=2.
The sequence is arithmetic with common difference d=−5.d=−5.

12.27

7 , 3 , −1 , −5 , −9 , 7 , 3 , −1 , −5 , −9 ,

12.28

11 , 3 , −5 , −13 , −21 , 11 , 3 , −5 , −13 , −21 ,

12.29

241

12.30

−106 −106

12.31

a11=2.a11=2. The general term is an=−3n+35.an=−3n+35.

12.32

a19=−55.a19=−55. The general term is an=−4n+21.an=−4n+21.

12.33

a1=5,a1=5,d=4.d=4. The general term is an=4n+1.an=4n+1.

12.34

a1=8,a1=8,d=−3.d=−3. The general term is an=−3n+11.an=−3n+11.

12.35

1,890

12.36

1,515

12.37

2,300

12.38

5,250

12.39

2,670

12.40

3,045

12.41

The sequence is geometric with common ratio r=3.r=3. The sequence is geometric with common ratio d=14.d=14. The sequence is not geometric. There is no common ratio.

12.42

The sequence is not geometric. There is no common ratio. The sequence is geometric with common ratio r=2.r=2. The sequence is geometric with common ratio r=12.r=12.

12.43

7 , −21 , 63 , −189 , 567 7 , −21 , 63 , −189 , 567

12.44

6 , −24 , 96 , −384 , 1536 6 , −24 , 96 , −384 , 1536

12.45

1 6,561 1 6,561

12.46

1 16,384 1 16,384

12.47

a9=39,366.a9=39,366. The general term is an=6(3)n1.an=6(3)n1.

12.48

a11=7,168.a11=7,168. The general term is an=7(2)n1.an=7(2)n1.

12.49

3,145,725 3,145,725

12.50

10,460,353,200 10,460,353,200

12.51

393,204 393,204

12.52

10,230 10,230

12.53

96

12.54

256 3 256 3

12.55

4 9 4 9

12.56

8 9 8 9

12.57

$ 10,000 $ 10,000

12.58

$ 3 , 333.33 $ 3 , 333.33

12.59

$ 88,868.36 $ 88,868.36

12.60

$ 698,201.57 $ 698,201.57

12.61

x 5 + 5 x 4 y + 10 x 3 y 2 + 10 x 2 y 3 x 5 + 5 x 4 y + 10 x 3 y 2 + 10 x 2 y 3
+ 5 x y 4 + y 5 + 5 x y 4 + y 5

12.62

p 7 + 7 p 6 q + 21 p 5 q 2 + 35 p 4 q 3 p 7 + 7 p 6 q + 21 p 5 q 2 + 35 p 4 q 3
+ 35 p 3 q 4 + 21 p 2 q 5 + 7 p q 6 + q 7 + 35 p 3 q 4 + 21 p 2 q 5 + 7 p q 6 + q 7

12.63

x 4 + 8 x 3 + 24 x 2 + 32 x + 16 x 4 + 8 x 3 + 24 x 2 + 32 x + 16

12.64

x 6 + 6 x 5 + 15 x 4 + 20 x 3 + 15 x 2 x 6 + 6 x 5 + 15 x 4 + 20 x 3 + 15 x 2
+ 6 x + 1 + 6 x + 1

12.65

16 x 4 96 x 3 + 216 x 2 216 x + 81 16 x 4 96 x 3 + 216 x 2 216 x + 81

12.66

64 x 6 192 x 5 + 240 x 4 160 x 3 64 x 6 192 x 5 + 240 x 4 160 x 3
+ 60 x 2 12 x + 1 + 60 x 2 12 x + 1

12.67

6 1 1 35

12.68

2 1 1 6

12.69

x 5 + 5 x 4 y + 10 x 3 y 2 + 10 x 2 y 3 x 5 + 5 x 4 y + 10 x 3 y 2 + 10 x 2 y 3
+ 5 x y 4 + y 5 + 5 x y 4 + y 5

12.70

m 6 + 6 m 5 n + 15 m 4 n 2 + 20 m 3 n 3 m 6 + 6 m 5 n + 15 m 4 n 2 + 20 m 3 n 3
+ 15 m 2 n 4 + 6 m n 5 + n 6 + 15 m 2 n 4 + 6 m n 5 + n 6

12.71

x 5 15 x 4 + 90 x 3 270 x 2 x 5 15 x 4 + 90 x 3 270 x 2
+ 405 x 243 + 405 x 243

12.72

y 6 6 y 5 + 15 y 4 20 y 3 + 15 y 2 y 6 6 y 5 + 15 y 4 20 y 3 + 15 y 2
6 y + 1 6 y + 1

12.73

243 x 5 810 x 4 y + 1080 x 3 y 2 243 x 5 810 x 4 y + 1080 x 3 y 2
720 x 2 y 3 + 240 x y 4 32 y 5 720 x 2 y 3 + 240 x y 4 32 y 5

12.74

256 x 4 768 x 3 y + 864 x 2 y 2 256 x 4 768 x 3 y + 864 x 2 y 2
432 x y 3 + 81 y 4 432 x y 3 + 81 y 4

12.75

15 x 4 y 2 15 x 4 y 2

12.76

8 a b 7 8 a b 7

12.77

7,168

12.78

280

Section 12.1 Exercises

1.

−5 , −3 , −1 , 1 , 3 −5 , −3 , −1 , 1 , 3

3.

4 , 7 , 10 , 13 , 16 4 , 7 , 10 , 13 , 16

5.

5 , 7 , 11 , 19 , 35 5 , 7 , 11 , 19 , 35

7.

1 , 5 , 21 , 73 , 233 1 , 5 , 21 , 73 , 233

9.

2 , 1 , 8 9 , 1 , 32 25 2 , 1 , 8 9 , 1 , 32 25

11.

1 , 3 2 , 5 4 , 7 8 , 9 16 1 , 3 2 , 5 4 , 7 8 , 9 16

13.

−2 , 4 , −6 , 8 , −10 −2 , 4 , −6 , 8 , −10

15.

1 , −4 , 9 , −16 , 25 1 , −4 , 9 , −16 , 25

17.

1 , 1 4 , 1 9 , 1 16 , 1 25 1 , 1 4 , 1 9 , 1 16 , 1 25

19.

a n = 8 n a n = 8 n

21.

a n = n + 5 a n = n + 5

23.

a n = e n + 2 a n = e n + 2

25.

a n = ( −1 ) n 5 n a n = ( −1 ) n 5 n

27.

a n = ( −1 ) n n 3 a n = ( −1 ) n n 3

29.

a n = ( −1 ) n 2 n a n = ( −1 ) n 2 n

31.

a n = 1 4 n a n = 1 4 n

33.

a n = n n + 1 a n = n n + 1

35.

5 2 n 5 2 n

37.

4 , 2 , 2 3 , 1 6 , 1 30 4 , 2 , 2 3 , 1 6 , 1 30

39.

3 , 6 , 18 , 72 , 360 3 , 6 , 18 , 72 , 360

41.

2 , 24 , 720 , 40320 , 3628800 2 , 24 , 720 , 40320 , 3628800

43.

1 , 1 2 , 1 3 , 1 4 , 1 5 1 , 1 2 , 1 3 , 1 4 , 1 5

45.

1 , 1 2 , 2 3 , 3 2 , 24 5 1 , 1 2 , 2 3 , 3 2 , 24 5

47.

2 , 3 2 , 8 3 , 15 2 , 144 5 2 , 3 2 , 8 3 , 15 2 , 144 5

49.

1 + 4 + 9 + 16 + 25 = 55 1 + 4 + 9 + 16 + 25 = 55

51.

5 + 7 + 9 + 11 + 13 + 15 = 60 5 + 7 + 9 + 11 + 13 + 15 = 60

53.

2 + 4 + 8 + 16 = 30 2 + 4 + 8 + 16 = 30

55.

4 1 + 4 1 + 4 2 + 4 6 + 32 3 = 10 2 3 4 1 + 4 1 + 4 2 + 4 6 + 32 3 = 10 2 3

57.

2 + 6 + 12 + 20 + 30 = 70 2 + 6 + 12 + 20 + 30 = 70

59.

1 2 + 2 3 + 3 4 + 4 5 + 5 6 = 71 20 1 2 + 2 3 + 3 4 + 4 5 + 5 6 = 71 20

61.

n = 1 5 1 3 n n = 1 5 1 3 n

63.

n = 1 5 1 n 3 n = 1 5 1 n 3

65.

n = 1 5 2 n n = 1 5 2 n

67.

n = 1 5 ( −1 ) n + 1 3 n n = 1 5 ( −1 ) n + 1 3 n

69.

n = 1 10 ( −1 ) n 2 n n = 1 10 ( −1 ) n 2 n

71.

n = 1 7 ( 2 n + 12 ) n = 1 7 ( 2 n + 12 )

73.

Answers will vary.

75.

Answers will vary.

Section 12.2 Exercises

77.

The sequence is arithmetic with common difference d=8.d=8.

79.

The sequence is not arithmetic.

81.

The sequence is arithmetic with common difference d=−3.d=−3.

83.

11 , 18 , 25 , 32 , 39 11 , 18 , 25 , 32 , 39

85.

−7 , −3 , 1 , 5 , 9 −7 , −3 , 1 , 5 , 9

87.

14 , 5 , −4 , −13 , −22 14 , 5 , −4 , −13 , −22

89.

163 163

91.

131 131

93.

−79 −79

95.

a20=−34.a20=−34. The general term is an=−2n+6.an=−2n+6.

97.

a11=59.a11=59. The general term is an=5n+4.an=5n+4.

99.

a8=−13.a8=−13. The general term is an=−5n+27.an=−5n+27.

101.

a1=11,a1=11,d=3.d=3. The general term is an=3n+8.an=3n+8.

103.

a1=21,a1=21,d=−8.d=−8. The general term is an=−8n+29.an=−8n+29.

105.

a1=−15,a1=−15,d=3.d=3. The general term is an=3n18.an=3n18.

107.

1,635

109.

−1 , 065 −1 , 065

111.

360

113.

6,325

115.

–3,575

117.

6,280

119.

4,125

121.

−3,850 −3,850

123.

Answers will vary.

125.

Answers will vary.

Section 12.3 Exercises

127.

The sequence is geometric with common ratio r=4.r=4.

129.

The sequence is geometric with common ratio r=12.r=12.

131.

The sequence is geometric with common ratio r=−2.r=−2.

133.

The sequence is geometric with common ratio r=12.r=12.

135.

The sequence is arithmetic with common difference d=5.d=5.

137.

The sequence is geometric with common ratio r=12.r=12.

139.

4 , 12 , 36 , 108 , 324 4 , 12 , 36 , 108 , 324

141.

−4 , 8 , −16 , 32 , −64 −4 , 8 , −16 , 32 , −64

143.

27 , 9 , 3 , 1 , 1 3 27 , 9 , 3 , 1 , 1 3

145.

472,392 472,392

147.

3,072

149.

0.0001 0.0001

151.

a9=2,304.a9=2,304. The general term is an=9(2)n1.an=9(2)n1.

153.

a15=219,683.a15=219,683. The general term is an=−486(13)n1.an=−486(13)n1.

155.

a10=0.000000001.a10=0.000000001. The general term is an=(0.1)n1.an=(0.1)n1.

157.

57,395,624 57,395,624

159.

−65,538 −65,538

161.

7,174,453 59,049 121.5 7,174,453 59,049 121.5

163.

65,534 65,534

165.

4088 4088

167.

29,524 6561 4.5 29,524 6561 4.5

169.

3 2 3 2

171.

9 2 9 2

173.

no sum as r1r1

175.

2,048

177.

1 3 1 3

179.

7 9 7 9

181.

5 11 5 11

183.

$6666.67$6666.67 $4000$4000 $15,000$15,000 $7500$7500

185.

$ 295,581.88 $ 295,581.88

187.

$ 14,234.10 $ 14,234.10

189.

Answers will vary.

191.

Answers will vary.

Section 12.4 Exercises

193.

a 8 + 8 a 7 b + 28 a 6 b 2 + 56 a 5 b 3 a 8 + 8 a 7 b + 28 a 6 b 2 + 56 a 5 b 3
+ 70 a 4 b 4 + 56 a 3 b 5 + 28 a 2 b 6 + 70 a 4 b 4 + 56 a 3 b 5 + 28 a 2 b 6
+ 8 a b 7 + b 8 + 8 a b 7 + b 8

195.

p 9 + 9 p 8 q + 36 p 7 q 2 + 84 p 6 q 3 p 9 + 9 p 8 q + 36 p 7 q 2 + 84 p 6 q 3
+ 126 p 5 q 4 + 126 p 4 q 5 + 84 p 3 q 6 + 126 p 5 q 4 + 126 p 4 q 5 + 84 p 3 q 6
+ 36 p 2 q 7 + 9 p q 8 + q 9 + 36 p 2 q 7 + 9 p q 8 + q 9

197.

a 6 6 a 5 b + 15 a 4 b 2 20 a 3 b 3 a 6 6 a 5 b + 15 a 4 b 2 20 a 3 b 3
+ 15 a 2 b 4 6 a b 5 + b 6 + 15 a 2 b 4 6 a b 5 + b 6

199.

x 3 + 15 x 2 + 75 x + 125 x 3 + 15 x 2 + 75 x + 125

201.

y 7 + 7 y 6 + 21 y 5 + 35 y 4 + 35 y 3 y 7 + 7 y 6 + 21 y 5 + 35 y 4 + 35 y 3
+ 21 y 2 + 7 y + 1 + 21 y 2 + 7 y + 1

203.

z 6 12 z 5 + 60 z 4 160 z 3 + 240 z 2 z 6 12 z 5 + 60 z 4 160 z 3 + 240 z 2
192 z + 64 192 z + 64

205.

243 x 5 405 x 4 + 270 x 3 90 x 2 243 x 5 405 x 4 + 270 x 3 90 x 2
+ 15 x 1 + 15 x 1

207.

27 x 3 135 x 2 + 225 x 125 27 x 3 135 x 2 + 225 x 125

209.

27 x 3 + 135 x 2 y + 225 x y 2 + 125 y 3 27 x 3 + 135 x 2 y + 225 x y 2 + 125 y 3

211.

7 1 1 45

213.

4 1 1 55

215.

m 5 + 5 m 4 n + 10 m 3 n 2 + 10 m 2 n 3 m 5 + 5 m 4 n + 10 m 3 n 2 + 10 m 2 n 3
+ 5 m n 4 + n 5 + 5 m n 4 + n 5

217.

s 7 + 7 s 6 t + 21 s 5 t 2 + 35 s 4 t 3 s 7 + 7 s 6 t + 21 s 5 t 2 + 35 s 4 t 3
+ 35 s 3 t 4 + 21 s 2 t 5 + 7 s t 6 + t 7 + 35 s 3 t 4 + 21 s 2 t 5 + 7 s t 6 + t 7

219.

y 4 12 y 3 + 54 y 2 108 y + 81 y 4 12 y 3 + 54 y 2 108 y + 81

221.

q 3 12 q 2 + 48 q 64 q 3 12 q 2 + 48 q 64

223.

625 x 4 1000 x 3 y + 600 x 2 y 2 625 x 4 1000 x 3 y + 600 x 2 y 2
160 x y 3 + 16 y 4 160 x y 3 + 16 y 4

225.

243 x 5 + 1620 x 4 y + 4320 x 3 y 2 243 x 5 + 1620 x 4 y + 4320 x 3 y 2
+ 5760 x 2 y 3 + 3840 x y 4 + 1024 y 5 + 5760 x 2 y 3 + 3840 x y 4 + 1024 y 5

227.

126 a 5 b 4 126 a 5 b 4

229.

462 x 5 y 6 462 x 5 y 6

231.

112

233.

324

235.

30,618

237.

Answers will vary.

239.

Answers will vary.

Review Exercises

241.

7 , 13 , 31 , 85 , 247 7 , 13 , 31 , 85 , 247

243.

3 4 , 5 16 , 7 64 , 9 256 , 11 1024 3 4 , 5 16 , 7 64 , 9 256 , 11 1024

245.

a n = 9 n a n = 9 n

247.

a n = e n 4 a n = e n 4

249.

a n = n n + 2 a n = n n + 2

251.

1 6 , 1 12 , 1 20 , 1 30 , 1 42 1 6 , 1 12 , 1 20 , 1 30 , 1 42

253.

−3 + ( −1 ) + 1 + 3 + 5 −3 + ( −1 ) + 1 + 3 + 5
+ 7 + 9 = 21 + 7 + 9 = 21

255.

4 + 4 + 2 + 2 3 + 1 6 = 65 6 4 + 4 + 2 + 2 3 + 1 6 = 65 6

257.

n = 1 5 ( −1 ) n 1 3 n n = 1 5 ( −1 ) n 1 3 n

259.

n = 1 5 4 n n = 1 5 4 n

261.

The sequence is arithmetic with common difference d=6.d=6.

263.

5 , 8 , 11 , 14 , 17 5 , 8 , 11 , 14 , 17

265.

−13 , −7 , −1 , 5 , 11 −13 , −7 , −1 , 5 , 11

267.

−129 −129

269.

a18=103.a18=103. The general term is an=7n23.an=7n23.

271.

a1=1,a1=1,d=4.d=4. The general term is an=4n3.an=4n3.

273.

−430 −430

275.

585 585

277.

4850 4850

279.

980 980

281.

The sequence is not geometric.

283.

The sequence is geometric with common ratio r=−2.r=−2.

285.

128 , 32 , 8 , 2 , 1 2 128 , 32 , 8 , 2 , 1 2

287.

1,536 1,536

289.

a12=−25,165,824.a12=−25,165,824. The general term is an=6(−4)n1.an=6(−4)n1.

291.

5,460

293.

3906.25 3906.25

295.

189 8 = 23.625 189 8 = 23.625

297.

343 6 57.167 343 6 57.167

299.

4 11 4 11

301.

$ 1,634,421.27 $ 1,634,421.27

303.

x 4 4 x 3 y + 6 x 2 y 2 4 x y 3 + y 4 x 4 4 x 3 y + 6 x 2 y 2 4 x y 3 + y 4

305.

32 y 5 240 y 4 + 720 y 3 1080 y 2 32 y 5 240 y 4 + 720 y 3 1080 y 2
+ 810 y 243 + 810 y 243

307.

11 1 1 56

309.

1 1 1 55

311.

t 9 9 t 8 + 36 t 7 84 t 6 + 126 t 5 t 9 9 t 8 + 36 t 7 84 t 6 + 126 t 5
126 t 4 + 84 t 3 36 t 2 + 9 t 1 126 t 4 + 84 t 3 36 t 2 + 9 t 1

313.

256 x 4 + 768 x 3 y + 864 x 2 y 2 256 x 4 + 768 x 3 y + 864 x 2 y 2
+ 432 x y 3 + 81 y 4 + 432 x y 3 + 81 y 4

315.

84 a 6 b 3 84 a 6 b 3

317.

135

319.

280

Practice Test

321.

1 4 , 1 5 , 1 6 , 1 7 , 1 8 1 4 , 1 5 , 1 6 , 1 7 , 1 8

323.

−4 + 16 64 + 256 = 204 −4 + 16 64 + 256 = 204

325.

−13 , −10 , −7 , −4 , −1 −13 , −10 , −7 , −4 , −1

327.

a23=59.a23=59. The general term is an=3n10.an=3n10.

329.

1,325 1,325

331.

3,260 3,260

333.

The sequence is geometric with common ratio r=13.r=13.

335.

5,242,880 5,242,880

337.

797,162 797,162

339.

5 6 5 6

341.

$ 1,409,344.19 $ 1,409,344.19

343.

8 1 1 210

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