Question

A sequence has its first term equal to 8, and each term of the sequence is obtained by adding 6 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 choices:
f(1) = 6 and f(n) = f(n − 1) + 8; n > 1

f(1) = 8 and f(n) = f(n − 1) + 6; n > 1

f(1) = 8 and f(n) = f(n − 1) + 6n; n > 1

f(1) = 6 and f(n) = f(n − 1) + 8n; n > 1

Answer 1

"First term equal to 8" means f(1) = 8
This is f(n) when n = 1

The nth term f(n) is found by adding 6 to the previous term f(n-1)
Which is why the recursive step is written as
f(n) = f(n-1) + 6

Put together, the rule is
f(1) = 8
f(n) = f(n-1)+6, when n > 1

So choice B is the answer