Mathematics Problem Of the Week

Spring 2002

POW #6

Fibonacci Quads

The Fibonacci sequence starts with F₁=1 and F₂=1 and then gets each new term in the sequence by adding the previous two. So F₃=1+1=2, F₄=2+1=3, F₅=3+2=5 and in general F_n+1=F_n+F_n-1.

The first few terms in the sequence are

1 1 2 3 5 8 13 21 34 55 89 144 ...

Take any four consecutive Fibonacci numbers. Compare the product of the first and last numbers in the quad to the product of the middle two. What do you find?

State (and prove) a theorem about Fibonacci numbers that is inspired by these comparisons.

Due Friday, March 8^th at Noon.