EXERCISES
For more exercises, see Extra Practice.
Practice and Problem Solving
A
Practice by Example
Example 1
(page 688)
Example 2
(page 689)
0
y.
What is the common difference of each arithmetic sequence?
1. 5, 4, 3, 2, . . .
1
4. 80, 60, 40, 20, . . .
2. 4, 11, 18, 25, . . . 7
3. 7, 1, -5, -11, . . .
5. 3, 9, 15, 21, . . . 6
6. -6, -5, -4, -3, . . .
6
1
Find the next three terms of each sequence. Then write a rule to
describe the sequence.
7. 0, 5, 10, 15, . . .
8. 21, 15, 9, 3, . . .
9. -11,-8,-5,-2,. . .
10. Exercising You begin doing 20 sit-ups every day in November.
You do 32 sit-ups every day in December, 44 sit-ups every day in
January, and so on. Find the next three terms of the sequence.
Then write a rule to describe the sequence.
y.
Example 3
(page 689)
Find the common ratio and the next three terms of each sequence.
Then write a rule to describe the sequence.
11. 3, 6, 12, 24, c
14. 2, 3, 4 12, 6 34, c
Example 4
(page 690)
B
Apply Your Skills
1,c
12. 5, 1, 15, 25
15. 12, 4, 113, 49, c
13. 45, 90, 180, 360, c
16. 8, 40, 200, 1,000, c
Tell whether each sequence is arithmetic, geometric, or neither. Find
the next three terms of the sequence.
17. 1, 3, 9, 27, c
18. 10, 5, 0, -5, c
19. 4.5, 4, 3.5, 3, c
20. 2, 2, 4, 6, c
21. -1, 3, -9, 27, c 22. 0, 5, 12, 21, c
Tell whether each sequence is arithmetic or geometric. If arithmetic,
give the common difference. If geometric, give the common ratio.
23. 1, 1 12, 2, 2 12, . . .
24. -3, -15, -75, . . . 25. -4, 12, -36, 108, . . .
26. 5, 6.4, 7.8, 9.2, . . . 27. 5, 15, 45, 135, c 28. 8.3, 5.7, 3.1, 0.5, . . .
Find the next three terms of each sequence. Then write a rule to
describe the sequence.
29. 1, 4, 16, 64, c
30. 3, 1, -1, -3, c
31. 2, 20, 200, 2,000, c
32. 9, 18, 36, 72, c
33. 25, 50, 75, 100, c 34. 6.5, 6.7, 6.9, 7.1, c
Tell whether each sequence is arithmetic, geometric, or neither. Find
the next three terms of each sequence.
35. 12, 56, 116, 1 12, c
36. 1, 10, 2, 20, c
37. 13, 12, 10, 7, c
1
1, 2 1, 2 1,c
38. 7, 7.03, 7.06, 7.09, c
39. 2 5, 2 10
20
40
40.
Writing in Math The first two numbers of a sequence are 4 and 8.
Can you tell what kind of sequence this is? Explain.
13-1 Patterns and Sequences
691-692
C
Challenge
Evaluate each expression for n 5 –2, –1, 0, and 1. Is the sequence
formed arithmetic, geometric, or neither?
41. 3n
Need Help?
To review compound
interest, see Lesson 7-8.
42. n(n + 1)
43. 2n
44. n2
45. Savings You open a savings account with $2,000. The account earns
4% interest compounded semiannually.
a. Write the balance in the savings account after each interest
payment for two years.
b. Does the pattern of balances form an arithmetic or geometric
sequence? Explain.
46. Patterns In the Fibonacci sequence 1, 1, 2, 3, 5, 8, c, you find
each term (after the first two terms) by adding the two previous
terms. Write the next three terms of the sequence.
Test Prep
Multiple Choice
47. If the first term of an arithmetic sequence is 35 and the fifth term
is 67, what is the third term?
A. 43
B. 51
C. 59
D. 75
48. If the rule for a sequence is “start with -7 and multiply by -2
repeatedly,” what is the fourth term in the sequence?
F. -112
G. -56
H. 56
I. 112
Reading Comprehension
Read the passage below before doing Exercises 49 and 50.
Population Watch
The population of the United States in 1980 was about 226
million, in 1985 it was about 238 million, in 1990 it was about
250 million, and in 1995 it was about 263 million.
Take It to the NET
Online lesson quiz at
www.PHSchool.com
49. What intervals of time are used with the given population data?
50. Which type of sequence, arithmetic or geometric, could you use to
model the United States population data? Explain.
Web Code: ada-1301
Mixed Review
Lesson 12-8
Lesson 9-6
51. Surveys You want to find out which presidential candidate is
most popular in your city. You plan to interview people who visit
the city’s art museum. State whether the survey plan describes a
good sample. Explain your reasoning.
Find the circumference of each circle rounded to the nearest tenth.
52. radius = 8.5 m
691-692
53. radius = 5 in.
Chapter 13 Nonlinear Functions and Polynomials
54. diameter = 14 cm