VMO 2010 Problem 2

Let $\{a_{n}\}$ be a sequence which satisfy $a_{1}=5$ and $a_{n=}\sqrt[n]{a_{n-1}^{n-1}+2^{n-1}+2.3^{n-1}} \forall n\geq2$ (a) Find the general fomular for $a_{n}$ (b) Prove that $\{a_{n}\}$ is decreasing sequences