## What is Fibonacci Series

In mathematics, the Fibonacci numbers, often known as **F _{n}**, form a series in which each number is the sum of the two numbers before it.

The Fibonacci numbers were originally mentioned in Indian mathematics in Pingala’s work on listing potential Sanskrit poetry patterns made up of syllables of two lengths, which was completed in 200 BC.

They were first used in Western European mathematics in the book Liber Abaci, published in 1202, by the Italian mathematician Leonardo of Pisa, afterwards known as Fibonacci.

Every term in a Fibonacci series is the sum of the previous two terms.

## Fibonacci Series Formula

The missing words in a Fibonacci series can be located using the mathematic formula for the series.

The Fibonacci series’s first two terms are 0 and 1. It will go to infinity. Some older versions of Fibonacci removed 0 from the series, but the original Fibonacci series is 0, 1, 1, 2, 3, 5, 8, 13,…..

For finding the (n+1)^{th }term in series, we need to use this recursive formula :-

**F _{n} = F_{n-1} + F_{n-2 } Where, n > 1;**

The value of n is always more than 2 because F0 and F1 are provided by default. First term F_{0} is 0 and second term F_{1} is 1 afterward F_{2} is found from the Fibonacci Formula.

F2 = F1 + F0 = 0 + 1 = 1

F3 = F2 + F1 = 1 + 1 = 2

## Fibonacci Series List

The first 20 numbers in the Fibonacci series are listed below.

F_{0} = 0 |
F_{10} = 55 |

F_{1} = 1 |
F_{11} = 89 |

F_{2} = 1 |
F_{12} = 144 |

F_{3} = 2 |
F_{13} = 233 |

F_{4} = 3 |
F_{14} = 377 |

F_{5} = 5 |
F_{15} = 610 |

F_{6} = 8 |
F_{16} = 987 |

F_{7} = 13 |
F_{17} = 1597 |

F_{8} = 21 |
F_{18} = 2584 |

F_{9} = 34 |
F_{19} = 4181 |

## Fibonacci Series Spiral

Fibonacci spiral is start in rectangle plane whose dimension follows the principle of a Golden Ratio.

## Application of Fibonacci Series

- It is applied in various fields like quantum mechanics, cryptography, etc.
- It is used to study various special mathematical sequences and also used for grouping
- Fibonacci Series helps in coding. For example it is helpful in finding computational run-time analysis of Euclid’s algorithm.