Fibonacci sequence

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Golden Ratio
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The Fibonacci Sequence is a sequence defined by a simple relationship.

Each term in the sequence is the sum of the previous to terms, ie

 f_n=f_{n-1}+f_{n-2} .

Traditionally, the first two values of the Fibonacci sequence are set as  f_1=1 , and  f_2=1 . This defines the entire rest of the sequence, since  f_3=f_2+f_1=1+1=2 .

We see that  f_4=f_3+f_2=2+1=3 .

The first few terms are 1,1,2,3,5,8,13,21,34...

This is the sequence of numbers someone is referring two if they say the Fibonacci Sequence, since it is the most common one.



It is possible to get slightly different sequences using different first values. For example, taking  f_1=-3 and  f_2=5 , we get the sequence -3,5,2,7,9,16,25,41,66,107...

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