Let the Fibonacci sequence Fn be defined by its recurrence relation (1) Fn=F(n-1)+F(n-2) for n>=3. Show that there is a unique way to extend the definition of Fn to integers n<=0 such that (1) holds for all integers n, and obtain an explicit formula for the terms Fn with negative indices n.

I am completely stuck on how to prove this by induction. I figured that Fn = Fn+2-Fn+1, but i don't know how to apply induction to this to prove it for all integers n