Question

If f(1)=7 and f(n)=3f(n-1)+3 then find the value of (3)

Answer 1

Given:

$f(1)=7$

$f(n)=3f(n-1)+3$

To find:

The value of f(3).

Solution:

We have,

$f(n)=3f(n-1)+3$               ...(i)

Substituting $n=2$ in (i), we get

$f(2)=3f(2-1)+3$

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

Substituting $f(1)=7$ in the above equation, we get

$f(2)=3(7)+3$

$f(2)=21+3$

$f(2)=24$

Now, substituting $n=3$ in (i), we get

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

$f(3)=3f(2)+3$

Substituting $f(2)=24$ in the above equation, we get

$f(3)=3(24)+3$

$f(3)=72+3$

$f(3)=75$

Therefore, the value of f(3) is 75.