## Fibonacci Sequence

This algorithm creates a list of Fibonacci numbers to the nth term. Choose the quantity of terms (3 - 100) for the algorithm output.

Background

The Fibonacci Sequence is a series of numbers starting with 0 and 1 (or 1 and 1) where a new number in the series is determined by the sum of the previous pair. Hence the series 0, 1, 1, 2, 3, 5, 8, 13, 21... because 0+1 = 1, 1+1 = 2, 1+2 = 3, and 2+3 = 5... The Fibonacci series was published in The Liber Abaci by Leonardo of Pisa in 1202. There are many reasons why this series inspires so much interest. One interesting aspect about the series is its ability to approximate phi (1.61803...) by observing the ratios of each successive pair of numbers. For example, 5/3 is 1.666 and 8/5 is 1.60. As the numbers of the Fibonacci series increase, the ratio of the pairs create a more accurate approximation of phi. Additional aspects are:

1) No two consecutive terms will share the same factor (divisor).

2) Any term in the sequence minus 1 is equal to the sum of other Fibonacci numbers in sequence or in even groups.