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.
The Attempt at a Solution
So I know the solution uses induction, and I think the first few negative terms should be F-1=-1, F-2=-1, F-3=-2 etc. So for the negative integers, Fn=F(n+1) + F(n+2) for n<0, but if the formula is supposed to extend to all integers n, that formula doesn't work...am I thinking about this problem wrong?