Mean of Fibonacci and Lucas numbers

Statement

The arithmetic mean of $F_n$ and $L_n$ is $F_{n+1}$. Verify it for $n=6$.

Solution

With $n=6$: $F_6=8$ and $L_6=18$, so $\frac{F_6+L_6}{2}=\frac{8+18}{2}=\frac{26}{2}=\boxed{13}=F_7.$