Fibonacci sequence

Nov 2012
2
0
LONDON
Hi can anyone explain how i can get express Fn+3 in terms of Fn+2 and Fn to show that Fn+2 = 1/2(Fn+3 + Fn). Any help is much appreciated
 
Dec 2011
2,314
916
St. Augustine, FL.
I would begin with:

(1) \(\displaystyle F_{n+2}=F_{n+1}+F_{n}\)

(2) \(\displaystyle F_{n+3}=F_{n+2}+F_{n+1}\)

Now, solve (2) for \(\displaystyle F_{n+1}\) and substitute into (1), then solve for \(\displaystyle F_{n+2}\).
 
  • Like
Reactions: 1 person