Question

If f(1) = 4 and f(n) = -4f(n-1) then find the value of ƒ (4).

Answer 1

F(4) = -256

Explanation:

f(1)=4

f(2)= -4* f(1) = -4 *4 = -16 F(2 ) = -16

f(3) = -4* f(2) = -4* (-16) = 64 F(3) = 64

f(4) = -4* f(3) = -4* 64 = -256 F(4) = -256

Answer 2

f(4) = -256

Explanation:

A recursive formula defines the nth term of a sequence based on the values of earlier terms.

To find the value of f(4) using the given recursive formula, we can work our way up from f(1) using the formula repeatedly.

Given recursive rule:

`\begin{cases}f(1)=4\\f(n)=-4f(n-1)\end{cases}`

To find f(2):

`\begin{aligned}f(2)&=-4f(2-1)\\&=-4f(1)\\&=-4 \cdot 4\\&=-16\end{aligned}`

To find f(3):

`\begin{aligned}f(3)&=-4f(3-1)\\&=-4f(2)\\&=-4 \cdot -16\\&=64\end{aligned}`

To find f(4):

`\begin{aligned}f(4)&=-4f(4-1)\\&=-4f(3)\\&=-4 \cdot 64\\&=-256\end{aligned}`

Therefore, the value of f(4) is -256.