I have to find the general term f(n), n>= 1, for the recurrence relation

f(n) = 3f(n-1), with f(1) = 4

I assume there is a formula or a set of rules to follow but I can not decifer it from my notes.

So I used a bit of trial and error + algebra

f(1) = 4

f(2) = 3*f(2-1) = 3*f1 = 12

f(3) = 3*f(3-1) = 3*f2 = 36

f(4) = 3*f(4-1) = 3*f3 = 108

so

$\displaystyle \frac{4}{3} * \frac{3}{1} = \frac{12}{3} = \frac{f(2)}{3}$ = f(1)

$\displaystyle \frac{36}{3} = \frac{f(3)}{3}$ = f(2)

$\displaystyle \frac{180}{3} = \frac{f(4)}{3}$ = f(3)

therefore

$\displaystyle f(n) = \frac{f(n+1)}{3} $ <-- the general term

is this ok?