Chapter 8 Arithmetic and Geometric sequences
Multiple Choice
Identify the choice that best completes the statement or answers the question.
Is the sequence arithmetic? If so, identify the common difference.
____
1. 13, 20, 27, 34, ...
b. yes; –7
a. yes; 7
____
c. yes; 13
d. no
2. Write a recursive formula for the sequence 7, 13, 19, 25, 31, ... Then find the next term.
a.
b.
c.
d.
; 37
;7
; –23
; 37
Generate the first five terms in the sequence using the explicit formula.
____
3.
a.
b.
c.
d.
____
4. What is the
a.
b.
c.
d.
____
–30, –25, –20, –15, –10
30, 25, 20, 15, 10
–10, –15, –20, –25, –30
10, 15, 20, 25, 30
term in the sequence using the given formula?
14
57
44
–44
5. Write a recursive formula for the sequence 7, 4, 1, –2, –5, .... Then find the next term.
a.
b.
c.
d.
Math Basic Course
;7
; –8
; 22
; –8
Chapter 8
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____
6. Write an explicit formula for the sequence 8, 6, 4, 2, 0, ... Then find
a.
b.
____
; –16
; –18
b. –343
8. Find the 110 term of the sequence
c. –338
d. –331
, 3, 13, 23, ...
b. –1097
a. 1083
____
; –20
; –18
c.
d.
7. Find the 50th term of the sequence 5, –2, –9, –16, ...
a. –352
____
.
c. 1093
d. 40
9. The table shows the predicted growth of a particular bacteria after various numbers of hours. Write an explicit
formula for the sequence of the number of bacteria.
Hours (n)
Number of
Bacteria
1
2
3
4
5
21
42
63
84
105
a.
b.
c.
d.
____ 10. Find the missing term of the arithmetic sequence 22, ___, 34, ...
a. 46
b. 16
c. 28
d. 40
____ 11. Find the 2nd and 3rd term of the sequence –7, ___, ___, –22, –27, ...
a. –12, –15
b. –17, –12
c. –10, –17
____ 12. Find the 5th term of the arithmetic sequence with
and
a. 5
b. 20
c. 15
d. –5
Math Basic Course
Chapter 8
d. –12, –17
.
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____ 13. A marching band formation consists of 8 rows. The first row has 5 musicians, the second has 7, the third has
9, and so on. How many musicians are in the last row?
a. 17 musicians
b. 19 musicians
c. 21 musicians
d. 96 musicians
Is the sequence geometric? If so, identify the common ratio.
____ 14. 6, 12, 24, 48, ...
b. yes; –2
a. yes; 2
c. yes; 4
d. no
Write the explicit formula for the geometric sequence. Then find the fifth term in the sequence.
____ 15.
,
,
; –64
; –64
a.
b.
c.
d.
; 128
; –512
What is the fifth term of the geometric sequence?
____ 16. 5, 15, 45, ...
a. 1215
b. 1875
____ 17.
c. 405
d. 3645
,
,
,
a. 0.87
b. 3.33
c. 25.2
d. 0.972
Math Basic Course
Chapter 8
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____ 18. Suppose you drop a tennis ball from a height of 8 feet. After the ball hits the floor, it rebounds to 80% of its
previous height. How high will the ball rebound after its third bounce? Round to the nearest tenth.
a. 3.3 feet
b. 4.1 feet
c. 5.1 feet
d. 1 feet
____ 19. Orlando is making a design for a logo. He begins with a square measuring 24 inches on a side. The second
square has a side length of 19.2 inches, and the third square has a side length of 15.36 inches. Which square
will be the first square with a side length of less than 12 inches?
a. fourth square
b. fifth square
c. sixth square
d. seventh square
What is a possible value for the missing term of the geometric sequence?
____ 20. 50, ___, 450, ...
a. 1350
b. 150
c. 3
d. 53
b. 650
c. 250
d. 125
____ 21. 1250, ___, 50, ...
a. 1200
____ 22. Find the 7th term of the geometric sequence with
and
a. 384
b. 112
c. 512
d. 256
Math Basic Course
Chapter 8
.
4|Page