Fibonacci sequence - calculating values

[Mokae]

Main Question or Discussion Point

Hello,
a couple of days back I have learn about calculating fibonacci sequences but still I don;t quite uderstand the way it is calcilated, could you please give me some thoughts about it?

Thank you

 

[grmnsplx]

it's easy
$$F_{n+1} = F_{n} + F_{n-1}$$

So the next number in the series, $$F_{n+1}$$, is the sum of the previous two numbers

We start with 1. 1 plus the previous number, 0, is 1. 1+0=1. Now our series is 1,1
Now we take 1 and the number before it, 1 and add. 1+1=2. Now our series is 1,1,2
Now we take 2 and the previous number, 1, and add. 2+1=3. Now our series is 1,1,2,3.
Now take 3 and add the previous number, 2, and add. 3+2=5. 1,1,2,3,5
5+3=8, 8+5=13, 13+8=21, ... Fib Series looks like 1,1,2,3,5,8,13,21,...

got it?

 

[Mokae]

Thank you,
my profesor teach me to use sqrt of 2 plus 5 all devide 2
to calculate and i don't understand why. I am too scare to ask him again

 

[Gib Z]

No, your teacher told you to use $\frac{\sqrt{5}+1}{2}$ to calculate Fibonnaci terms. That constant I just said is the golden ratio, commonly denoted by the greek letter "phi", $\phi$. It is used in the closed form expression of the terms in the sequence. Don't be asked, you should ask him again.

 

[tiny-tim]

… wikipedia … !

Hi Mokae!

If you don't understand something, wikipedia is usually a good place to look.

For the siginificance of √5 in Fibonacci numbers, look at:

http://en.wikipedia.org/wiki/Fibonacci_number. ​