Do You Know The Fibonacci rule?

Number Theory Level 2

Let F n F_n denote the n th n^\text{th} Fibonacci number , where F 0 = 0 , F 1 = 1 F_0 = 0, F_1 = 1 and F n = F n − 1 + F n − 2 F_n = F_{n-1} + F_{n-2} for n = 2 , 3 , 4 , … n=2,3,4,\ldots .

What is the value of F 13 F_{13} ?


The answer is 233.

View wiki
Rex Holmes by Rex Holmes , 17, USA

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Rishik Jain
Jun 24, 2016

F 2 n − 1 = F n − 1 2 + F n 2 F 13 = F 6 2 + F 7 2 F 13 = 169 + 64 = 233 F_{2n-1}=F_{n-1}^2+F_n^2 \\ F_{13}=F_6^2+F_7^2 \\ F_{13}=169+64=\boxed{233}

0 Helpful 0 Interesting 1 Brilliant 0 Confused

Moderator note:

Why does that work?

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...