Question

Which recursive formula can be used to generate the sequence shown, where f(1) = 9.6 and n > 1?

9.6, –4.8, 2.4, –1.2, 0.6, ...

f(n + 1) = –0.5f(n)
f(n + 1) = 0.5f(n)
f(n + 1) = f(0.5n)
f(n + 1) = f(–0.5n)

Answer 1

it is f(n + 1) = –0.5f(n)

Explanation:

I just took it on edge 2020

Answer 2

f(n + 1) = –0.5f(n)

Explanation:

The terms 9.6, –4.8, 2.4, –1.2, 0.6 alternate negative and positive. This means they must have a negative rate of change (because multiplying with negatives give both positive and negative numbers).

This narrows it down to:

f(n + 1) = –0.5f(n)

f(n + 1) = f(–0.5n)

Substitute f(n) for f(1)=9.6.

f(n + 1) = –0.5(n)

f(1 + 1) = –0.5(1)

f(2) = –0.5(9.6)

f(2) = -4.8

Since the second term is -4.8, f(n + 1) = –0.5f(n) is the recursive formula.