Theme: Generalising May 2004
5-1 Golden Fibs
The Fibonacci sequence F_n is defined by the relation

Fn+2=Fn + Fn+1

where F₀=0 and F₁=1.
Now suppose that we take the same relation and more general sequences X_n with any two starting values X₀ and X₁. Prove that the sequence is geometric if and only if the first two terms are in the ratio 1 : f where f is the golden ratio (1+Ö5)/2.