# Fibonacci sequence

• Mar 28th 2010, 03:36 AM
bigroo
Fibonacci sequence
I have from a previous question these answers:

Fn+3 = Fn+2 + Fn+1 & Fn = Fn+2 - Fn+1

I have to use these answers to show that:

Fn+3 + Fn = 2Fn+2 & Fn+3 - Fn = 2Fn+1 for n = 0, 1, 2,...

I'm not sure how to do this although I understand that the second set of statements are true.
Any help would be really appreciated :)
• Mar 28th 2010, 04:54 AM
CaptainBlack
Quote:

Originally Posted by bigroo
I have from a previous question these answers:

Fn+3 = Fn+2 + Fn+1 & Fn = Fn+2 - Fn+1

I have to use these answers to show that:

Fn+3 + Fn = 2Fn+2 & Fn+3 - Fn = 2Fn+1 for n = 0, 1, 2,...

I'm not sure how to do this although I understand that the second set of statements are true.
Any help would be really appreciated :)

You want to show that:

$F_{n+3}+F_n=2F_{n+2}$

You begin by using the recurrence for the Fibonacci numbers on $F_{n+3}$, then group terms if you try that and have further difficulties post what you have done and tell us what difficulties you are having with it.

CB