Fibonacci sequence

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Fibonacci sequence

In the Fibonacci sequence each term is the sum of the two preceding terms, so

and that gives then

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ...

Explanation

Processes of natural growth often develop according this series. After 0 and 1 the further development is

0 + 1 = 1

     1 + 1 = 2

         1 + 2 = 3

             2 + 3 = 5

                 3 + 5 = 8

                     5 + 8 = 13

                         8 + 13 = 21

                             13 + 21 = 34

                                  21 + 34 = 55

                                       34 + 55 = 89

                                            55 + 89 = 144

Example 1

You can generate this sequence in a number table from recursion between three terms as expressed by an+2=an+1+an, with initial terms of a1=1,a2=1, as n changes in value from 1 to 6.

Leonardo of Pisa (also known as Fibonacci) described it after examining fast-growing populations in the animal world. He is not the inventor, as the sequence was known already for many centuries in China and India.

In his book Liber Abaci (book of arithmetic) he described this sequence, which probably was known for hundreds of years.

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