f(n+1)=3f(n)/2 + 1/2, find f(p) in terms of p

[keen sandal]

$$f(n+1)=\frac12 (3f(n)+1)$$
Find $f(p)$ in terms of $p$ and $k$, given $f(1)=k$.

I managed to find summaton of $f(r)$ from $1$ to $p$ given the value of $f(p)$ but couldnt solve this specific question
but im not sure if its solvable or not either
this is again a personal endeavour of mine, not a problem given by my school or teachers.

[magic elm]

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[hollow saddle]

Huge Jacked Man

[worldly bear]

Search up how to solve linear recurrences

[keen sandal]

+close