Question

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

Answer 1

Answer:

$f(4) = 1280$

Step-by-step 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:

$f(4) = 2f(3)$

$f(4) = 2 * 640$

$f(4) = 1280$