Subject: Fibonacci's Sequence

What discoveries can be made about the sum of squares of Fibonacci's Sequence.


Middle School/Junior High

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Brief Research or Class Assignment

Hi Vandan, One fact that I know about the squares of the terms in the Fibonacci sequence is the following: Suppose that fn is the nth term in the Fibonacci sequence, then

(fn)2 + (fn + 1)2 = f2n + 1

This fact follows from a more general result that states:

For any natural number a,

fafn + fa + 1fn + 1 = fa + n + 1

for all natural numbers n.

This can be proved by mathematical induction.

To get the previous result let a = n.

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