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

Question

Mathematics

Abel Mitchell

29 December, 21:01

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

+2

Answers (1)

Know the Answer?

Emilee Lynn · 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