My Math Forum recurrence relation fn+4

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 December 4th, 2011, 08:09 AM #1 Member   Joined: Dec 2011 Posts: 75 Thanks: 0 recurrence relation fn+4 hey everyone really stuck on these two questions if anyone could help, with an explanation that would be great, as i dont understand really what the question is asking let alone the methods i would take. thanks Let Fn be the Fibonacci sequence. (a) (i) Use the Fibonacci recurrence relation to express both Fn+4 and Fn in terms of Fn+1 and Fn+2, for n = 0,1,2, . . .. (ii) Use your answer to part (a)(i) to show that Fn+4 + Fn = 3Fn+2 for n = 0,1,2, . . . .
 December 4th, 2011, 08:48 AM #2 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: recurrence relation fn+4 The Fibonacci sequence is defined recursively by: $F_{n+1}=F_{n}+F_{n-1}$ Thus: $F_{n+4}=F_{n+3}+F_{n+2}=F_{n+2}+F_{n+1}+F_{n+2}=2F _{n+2}+F_{n+1}$ $F_{n}=F_{n+2}-F_{n+1}$ Adding we find: $F_{n+4}+F_{n}=3F_{n+2}$ I have moved this topic to "Applied Mathematics, Set Theory, Logics and other."
 December 4th, 2011, 09:15 AM #3 Member   Joined: Dec 2011 Posts: 75 Thanks: 0 Re: recurrence relation fn+4 Thanks MarkFL, For your quick response and explanation, I've just joined this so wasn't too sure were to post it, again thanks for moving it to the right topic. [Now I] finally understand what i needed to do!
 December 4th, 2011, 09:22 AM #4 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: recurrence relation fn+4 Glad to help, and welcome to the forum! Sometimes it isn't clear which forum is best for a topic especially to new members.

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