Regents Review Sequences

In a sequence, the first term is 4 and the common difference is 3. The fifth term of this sequence is

• -11

• -8

• 16

• 19

If f(1) = 3 and f(n) = −2f(n − 1) + 1, then f(5) =

• 43

• -5

• 11

• 21

Given the function f(n) defined by the following:

f(1) = 2

f(n) = −5f(n − 1) + 2

Which set could represent the range of the function?

• {2,4,6,8,. . . }

• {2,−8,42,−208,. . . }

• {−8,−42,−208,1042,. . . }

• {−10,50,−250,1250,. . . }

Which recursively defined function represents the sequence 3,7,15,31,. . .?

• f(1) = 3, f(n + 1) = 2^f(n) + 3

• f(1) = 3, f(n + 1) = 2^f(n) - 1

• f(1) = 3, f(n + 1) = 2f(n) + 1

• f(1) = 3, f(n + 1) = 3f(n) − 2

Which function defines the sequence −6,−10,−14,−18,. . ., where f(6) = −26?

• f(x) = −4x − 2

• f(x) = 4x − 2

• f(x) = −x + 32

• f(x) = x − 26