Analyzing Graphs Answers

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Which best describes the relationship between the successive terms in the sequence below?–3.2, 4.8, –7.2, 10.8, …

A
The terms have a common difference of 8.
B
The terms have a common difference of 1.6.
C
The terms have a common ratio of –1.5.
D
The terms have a common ratio of –0.67.
3

Which sequences are arithmetic? Check all that apply.

A
–5, 5, –5, 5, –5, …
B
96, 48, 24, 12, 6
C
18, 5.5, –7, –19.5, –32, …
D
–1, –3, –9, –27, –81, …
E
16, 32, 48, 64, 80
4

Which sequences are geometric? Check all that apply.–2, –4, –6, –8, –10, …16, –8, 4, –2, 1–15, –18, –21.6, –25.92, –31.104, …4, 10.5, 17, 23.5, 30, …625, 125, 25, 5, 1, …

A
–2, –4, –6, –8, –10, …
B
16, –8, 4, –2, 1
C
–15, –18, –21.6, –25.92, –31.104, …
D
4, 10.5, 17, 23.5, 30, …
E
625, 125, 25, 5, 1, …
6

Which sequence could be partially defined by the recursive formula f (n + 1) = f(n) + 2.5 for n ≥ 1?

A
2.5, 6.25, 15.625, 39.0625, …
B
2.5, 5, 10, 20
C
–10, –7.5, –5, –2.5, …
D
–10, –25, 62.5, 156.25
7

Which recursive formula can be used to generate the sequence below, where f(1) = 3 and n ≥ 1?3, –6, 12, –24, 48, …

A
f (n + 1) = –3 f(n )
B
f (n + 1) = 3 f(n )
C
f (n + 1) = –2 f(n )
D
f (n + 1) = 2 f(n)
8

Which recursive formula can be used to generate the sequence below, where f(1) = 6 and n ≥ 1?6, 1, –4, –9, –14, …

A
f (n + 1) = f(n) + 5
B
f (n + 1) = f(n) – 5
C
f (n) = f(n + 1 ) – 5
D
f (n + 1) = –5f(n)
10

A bouncing ball reaches a height of 27 feet at its first peak, 18 feet at its second peak, and 12 feet at its third peak. Describe how a sequence can be used to determine the height of the ball when it reaches its fourth peak.

Answer:

There is a common ratio of 2/3 between the height of the ball at each bounce. So, the bounce heights form a geometric sequence: 27, 18, 12. Twothirds of 12 is 8, so on the fourth bounce, the ball will reach a height of 8 feet.

11

What did you include in your response? Check all that apply.

A
There is a common ratio between bounce heights.
B
Multiply 12 by 2/3.
C
The height on the fourth bounce is 8 feet.

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