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.$
Source: Ukraine 1997 grade 10
Tags: algebra proposed, algebra
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.$