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. $
Problem
Source: North Macedonian Mathematical Olympiad 1995 p1
Tags: Sequence, recurrence relation, algebra