Question

A sequence has its first term equal to 4, and each term of the sequence is obtained by adding 2 to the previous term. If f(n) represents the nth term of the sequence, which of the following recursive functions best defines this sequence?

Answer 1

A. f(1)=2 and f(n) = f(n-1)+4; n>1
B. f(1) =4 and f(n) = f(n-1)+2n; n>1
C. f(1) =2 and f(n) = f(n-1) +4n; n>1
D. f(1)=4 and f(n) = f(n-1) + 2; n >1
If you could please explain how to get the answer that would be a big help because I have no idea where to even start.

Answer 2

f(1) is the first term, so f(1) = 4.
The nth term is f(n), so the previous term would be f(n-1). For example, n = 6 for the sixth term, which is f(6). The term before that is the fifth term, f(5), which is the same as f(6 - 1).

Answer 3

To get each f(n) you need to add 2 to f(n - 1), so
f(n) = f(n -1) + 2

Answer 4

@peachpi so would the answer be B?

Answer 5

no. not +2n, just +2

Answer 6

OH. I think I get it now. Thank you so much.

Answer 7

you're welcome