Recognizing Patterns: Assignment

Three terms of an arithmetic sequence are shown below. Which recursive formula defines the sequence? f(1) = 6, f(4) = 12, f(7) = 18

C. f (n + 1) = f(n) + 2

A sequence is defined by the recursive formula f (n + 1) = f(n) - 2. If f(1) = 18, what is f(5)?

10

Which sequences are arithmetic? Check all that apply.

3. 18, 5.5, -7, -19.5, -32, ... 5. 16, 32, 48, 64, 80

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

C. -10, -7.5, -5, -2.5, ...

Which sequences are geometric? Check all that apply.

2. 16, -8, 4, -2, 1 3. -15, -18, -21.6, -25.92, -31.104, ... 5. 625, 125, 25, 5, 1, ...

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

C. The terms have a common ratio of -1.5.

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

C. f (n + 1) = -2 f(n )

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.

(Sample 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. Two-thirds of 12 is 8, so on the fourth bounce, the ball will reach a height of 8 feet.

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

B. f (n + 1) = f(n) - 5

What is the common difference between the elements of the arithmetic sequence below? -18, -22.5, -27, -31.5, -36

-4.5