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The Fibonacci Sequence


The Fibonacci sequence

The Fibonacci sequence is a well-known sequence whose first few terms are As shown, the first two terms are and and each subsequent term will be the sum of the previous two terms.

Fibonacci numbers in the Fibonacci sequence

For every term after the second term, the sequence can be expressed by the recursive rule:

This means that, in order to determine the fourth term of the sequence, , one must have the terms and . The sequence is named after the Italian mathematician Leonardo Fibonacci, who used it to describe how pairs of rabbits increases as they multiply under certain conditions. Sometimes, the first two numbers are defined as and This, however, does not change the sequence in any way other than by increasing the index of every term by one compared to the previously mentioned definition.