### Fibonnaci Again

Some facts are instances of a Great Principle, while others Just Are. Here is a nice example I take from a book by Martin Gardner, the great popularizer of math and science--Mathematics Magic and Mystery (Dover, 1956):

Write down the first ten terms of any Fibonacci sequence, e.g.: 7,2,9,11,20,... Their sum is 11 times the 7th term. This is easily proven by brute force: 1st term a, 2nd term b, 3rd term a+b, 4th term a+2b, etc. The sum of the first ten terms is 55a+88b; the 7th term is 5a+8b.

This just is. Examine the first few terms of ths sequence and you will not find more instances of like behavior.

1. scineram5:25 PM

"Examine the first few terms of ths sequence and you will not find more instances of like behavior."

Proof?

2. That was not intended as a math statement, merely as a human observation, viz., if you actually look at the first few terms--say, 10--you will not see any other similar relationship between any of the terms and any of the sums--at least, not if you are remotely like me in the way your mind works.