jmc

The Fibonacci numbers are defined recursively by the equation $$F_n=F_{n-1}+F_{n-2}$$for every integer $n\ge 2$, with initial values $F_0=0$ and $F_1=1$. Let $G_n=F_{3n}$ be every third Fibonacci number. There are constants $a$ and $b$ such that every integer $n\ge 2$ satisfies $$G_n=a{G}_{n-1}+b{G}_{n-2}.$$Find $(a,b)$.