Fibonacci sequence

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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...