Question

If f1) = 160 and f(n +1) =-2fn), what is f4)?

Answer 1

`f(4) = 1280`

Explanation:

Given

`f(1)= 160`

`f(n+1) = 2f(n)`

Required

Determine f(4)

Take n as 3:

`f(n+1) = 2f(n)` becomes

`f(3+1) = 2f(3)`

`f(4) = 2f(3)`

We need to get f(3).

Take n as 2

`f(n+1) = 2f(n)` becomes

`f(2+1) = 2f(2)`

`f(3) = 2f(2)`

We need to get f(2).

Take n as 1

`f(n+1) = 2f(n)` becomes

`f(1+1) = 2f(1)`

`f(2) = 2f(1)`

Substitute 160 for f(1)

`f(2) = 2 * 160`

`f(2) = 320`

Recall that:

`f(3) = 2f(2)`

`f(3) = 2 * 320`

`f(3) = 640`

Recall that:

`f(4) = 2f(3)`

`f(4) = 2 * 640`

`f(4) = 1280`