Question

The Fibonacci numbers are defined recursively by

F0=0,F1=1,
Fn=Fn−1+Fn−2 for n≥2.
Consider the sequence of every 3rd Fibonacci number, i.e. Gn=F3n. There are constants a and b such that
Gn=aGn−1+bGn−2
for every integer n≥2. What is a+b?