GS. 1 For all integers $n, F_{n}$ is defined by $F_{n}=F_{n-1}+F_{n-2}, F_{0}=0$ and $F_{1}=1$. If $a=F_{-5}+F_{-4}+\ldots+F_{4}+F_{5}$, find the value of $a$.
$\begin{array}{l}F_{2}=0+1=1, F_{3}=1+1=2, F_{4}=1+2=3, F_{5}=2+3=5 \\ F_{-1}+0=1 \Rightarrow F_{-1}=1, F_{-2}+1=0 \Rightarrow F_{-2}=-1, F_{-3}+(-1)=1 \Rightarrow F_{-3}=2 \\ F_{-4}+2=-1 \Rightarrow F_{-4}=-3, F_{-5}+(-3)=2 \Rightarrow F_{-5}=5 \\ a=F_{-5}+F_{-4}+\ldots+F_{4}+F_{5}=5-3+2-1+1+0+1+1+2+3+5=16\end{array}$