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#1 2006-11-15 09:19:30

Ricky Jones
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Fibonacci Sequence

Can anyone please explain how you work out the nth term for the Fibonacci Sequence. My maths teacher did explain but I got rather confused. Please Help.

#2 2006-11-15 11:57:53

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

Re: Fibonacci Sequence

The nth term in terms of n is very difficult to find. However, it is easy to express it in terms of the (n-1)th and (n-2)th term.

The Fibonacci sequence is defined by a[sub]1[/sub] = a[sub]2[/sub] = 1, and a[sub]n[/sub] = a[sub]n-1[/sub] + a[sub]n-2[/sub] for n>2.

So the first two numbers are both 1, the third is 1+1 = 2, the fourth is 1+2 = 3, then 2+3 = 5, 3+5 = 8, and so on.

Does that help?


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It wanted to be normal.

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#3 2006-11-15 14:41:08

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

Re: Fibonacci Sequence

The nth term in terms of n is very difficult to find.

Difficult to find, maybe.  You need to know a bunch of linear algebra before this is possible.  However, anyone who understands algebra can use the formula:


Edit:  Whoops, read the introductory post wrong.

Here is a fairly good link:

http://www.mcs.surrey.ac.uk/Personal/R. … proof.html


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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#4 2006-11-15 15:03:06

George,Y
Member
Registered: 2006-03-12
Posts: 1,379

Re: Fibonacci Sequence

Ricky, 2 should replace 2[sup]n[/sup] in your formula

Last edited by George,Y (2006-11-15 15:03:31)


X'(y-Xβ)=0

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