Question 164
Let $\left(a_{n}\right)_{n \geqslant 0}$ be a sequence of real numbers. Suppose that $a_{n}=\left|a_{n+1}-a_{n+2}\right|$ for every natural number $n$. Moreover, $a_{0}$ and $a_{1}$ are strictly positive and distinct. Prove that the sequence $\left(a_{n}\right)_{n \geqslant 0}$ is not bounded.