f(1) = 5, f(n) = (−8) · f(n − 1) + 15

Answer 1

I assume you want the general term.

It is (5/3) - (5/12)(-8)ⁿ

There may be other methods of solution, but the one I know involves the Calculus of Finite Differences; for more information see "Calculus of Finite Differences" by Jordan.