Question

If f(1) = 10 and f(n) = f(n = 1) – 4 then find the value of f(5).

Answer 1

Given:

$f(1)=10$ and $f(n)=f(n-1)-4$.

To find:

The value of f(5).

Solution:

We have,

$f(n)=f(n-1)-4$

For $n=2$,

$f(2)=f(2-1)-4$

$f(2)=f(1)-4$

$f(2)=10-4$

$f(2)=6$

For $n=3$,

$f(3)=f(3-1)-4$

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

$f(3)=6-4$

$f(3)=2$

For $n=4$,

$f(4)=f(4-1)-4$

$f(4)=f(3)-4$

$f(4)=2-4$

$f(4)=-2$

For $n=5$,

$f(5)=f(5-1)-4$

$f(5)=f(4)-4$

$f(5)=-2-4$

$f(5)=-6$

Therefore, the value of $f(5)$ is $-6$.