Why is 11 times the 7th term of a fibonacci series equal to the sum of 10 terms?
I was watching scam-school on youtube the other day and this number trick just astonished me. Can someone please explain why this works?
After a lot of searching, I've been stumbling onto slightly complicated mathematical explanations. An explanation of a simpler nature, one that a child can understand, would be much appreciated.
Also, Can you extend this to find the sum of n terms of a fibonacci type sequence?
Best Answer
As far as I know, it seems to be nothing more than coincidence. Say you have your starting numbers, $a$ and $b$. Your ten terms are $a,b,a+b,a+2b,2a+3b,3a+5b,5a+8b,8a+13b,13a+21b,21a+34b$
the sum of which is $55a+88b$, which just happens to $11$ times the seventh term in your sequence.