Write the first four terms of a sequence given the recursive rule below.

Question

f(n) = f(n-1)-4, for all n ≥ 2 and f(1) = 32

A. 32, 31, 30, 29

B. not enough information

C. 32, 28, 24, 20

D. 32, 27, 22, 17

Answer 1

Given the recursive rule:

f(n) = f(n - 1) - 4 for n ≥ 2 and f(1) = 32,

we can find the next terms by substituting n = 2, 3, 4. Just by looking at the recursive rule, we can tell that each term will be 4 less than the previous term since it has a -4 in the end. So, lets compute it:

n = 2:

f(2) = f(2 - 1) - 4 = f(1) - 4 = 32 - 4 = 28

n = 3:

f(3) = f(3 - 1) - 4 = f(2) - 4 = 28 - 4 = 24

n = 4:

f(4) = f(4 - 1) - 4 = f(3) - 4 = 24 - 4 = 20

So, the first four terms are: 32, 28, 24, 20 and option C is correct.

Answer 2

f(1) = -4 corresponds to 32, a difference of +28

f(2) = -3 corresponds to 31

f(3) = -2 corresponds to 30

f(4) = -1 corresponds to 29