TIFR-2013-Maths-D: 35

Question

True/False Question :

Let $\left \{ a_{n} \right \}$ be any non-constant sequence in $\mathbb{R}$ such that $a_{n+1}=\frac{a_{n}+a_{n+2}}{2}$ for all $n\geq 1$. Then $\left \{ a_{n} \right \}$ is unbounded.