Solving Linear Systems with Substitution - Definition & Examples

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 $$G_n = a G_{n - 1} + b G_{n - 2}.$$ What is $100a+b$?

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