# Fibonacci Numbers Calculator

'Cuemath's Fibonacci Numbers Calculator' is an online tool that helps to calculate the Fibonacci Sequence.

## What is the Fibonacci Numbers Calculator?

Cuemath's online Fibonacci Numbers Calculator helps you to calculate the Fibonacci Sequence in a few seconds.

## How to Use the Fibonacci Numbers Calculator?

Please follow the below steps to find the Fibonacci Sequence:

**Step 1:**Enter the number of terms to be displaced in the given input box.**Step 2:**Enter the limits in the given input box.**Step 3:**Click on the**"Calculate"**button to find the Fibonacci Sequence.**Step 4:**Click on the**"Reset"**button to clear the fields and find the Fibonacci Sequence for different limit values.

## How to Find the Fibonacci Numbers?

Fibonacci numbers are defined as a sequence of whole numbers arranged as follows: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34,...This sequence is called the Fibonacci sequence. Each number in the Fibonacci sequence is given as F_{n}. It is an infinite sequence.

The rules for the Fibonacci numbers are given as :

- The first number in the Fibonacci sequence is given as
**F**_{0}= 0 - The second number in the Fibonacci sequence is given as
**F**_{1}= 1 - Fibonacci numbers follow a rule according to which,
**F**, where n > 1_{n}= F_{(n-1)}+ F_{(n-2)} - The third number in the Fibonacci sequence is given, F
_{2 }= F_{1 }+ F_{0}= 1 + 0 = 1. The Fibonacci sequence goes like 0, 1, 1, and so on.

**Solved Example:**

Find the Fibonacci numbers for F_{0} = 2, and F_{1 }= 6 for 5 terms?

**Solution:**

Given: N = 5 terms, F_{0} = 2, F_{1 }= 6

Fibonacci numbers follow a rule according to which, F_{n} = F_{(n-1)} + F_{(n-2)} where n > 1

F_{2} = F_{(2-1)} + F_{(2-2)} = F_{1} + F_{0} = 6 + 2 = 8

F_{3} = F_{(3-1)} + F_{(3-2)} = F_{2} + F_{1} = 8 + 6 = 14

F_{4} = F_{(4-1)} + F_{(4-2)} = F_{3} + F_{2} = 14 + 8 = 22

F_{5 }= F_{(5-1)} + F_{(5-2)} = F_{4} + F_{3} = 22 + 14 = 36

Therefore, the Fibonacci series

F_{0} |
F_{1} |
F_{2} |
F_{3} |
F_{4} |
F_{5 } |

2 | 6 | 8 | 14 | 22 | 36 |

Therefore, the Fibonacci series are 2,6,8,14,22,36

Similarly, you can try the calculator to find the find the Fibonacci Sequence for

a) Number of terms = 10, F_{0} = 3 and F_{1} = 8

b) Number of terms = 15, F_{0} = 5 and F_{1} = 11

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