UA-UMO 1997 Problem 103

A sequence is defined by $a_1=a_2=a_3=1$ and $a_{n+3}=-a_n-a_{n+1}$ for all $n \in \mathbb{N}$ . Prove that this sequence is not bounded , i.e. that for every $M \in \mathbb{R}$ there is an $n$ for which $|a_n|>M.$