Squares of Fibonacci numbers

Subject: Fibonacci's Sequence

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

Vandan

Middle School/Junior High

Planned use of the information:

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 f_n is the n^th term in the Fibonacci sequence, then

(f_n)² + (f_{n + 1})² = f_{2n + 1}

This fact follows from a more general result that states:

For any natural number a,

f_af_n + f_{a + 1}f_{n + 1} = f_{a + n + 1}

for all natural numbers n.

This can be proved by mathematical induction.

To get the previous result let a = n.

Cheers,
Penny Go to Math Central