Question

A sequence is defined by the recursive function f(n + 1) = –10f(n).

If f(1) = 1, what is f(3)?

3
–30
100
–1,000

Answer 1

To find f(3) in the recursive sequence, we first calculate f(2) as –10, then apply the recursive formula again to obtain f(3) as 100.

Step-by-step explanation:

The question requires us to find the value of f(3) in a recursive sequence where f(n + 1) = –10f(n) and f(1) = 1. Since we are given the initial value, we can calculate the succeeding terms step-by-step.

For f(2), we use the recursive formula: f(2) = –10f(1) = –10(1) = –10.

Next, for f(3), we again apply the recursive formula: f(3) = –10f(2) = –10(–10) = 100.

Therefore, the value of f(3) is 100.