MK-MO 1995 Problem 1

Let $a_0$ be a real number. The sequence $\{a_n \}$ is given by $a_ {n + 1} = 3 ^ n-5a_n$ , $n = 0,1,2, \ldots$ . a) Express the general member $a_n$ through $a_0$ and $n.$ b) Find such $a_0,$ that $a_ {n + 1}> a_n,$ for every $n.$