Sum of neighboring Fibonacci numbers gives a Lucas number

Statement

The identity $F_{n-1}+F_{n+1}=L_n$ holds. Use it to compute $L_7$ from the Fibonacci numbers.

Solution

With $n=7$: $F_6=8$ and $F_8=21$, so $L_7=F_6+F_8=8+21=\boxed{29}.$