NL-NWO 1993 Problem 3

A sequence of numbers is defined by $u_1=a, u_2=b$ and $u_{n+1}=\frac{u_n+u_{n-1}}{2}$ for $n \ge 2$ . Prove that $\lim_{n\to\infty}u_n$ exists and express its value in terms of $a$ and $b$ .