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 F₀ = 0 
• The second number in the Fibonacci sequence is given as F₁ = 1
• Fibonacci numbers follow a rule according to which, F_n = F_(n-1) + F_(n-2) , where n > 1
• The third number in the Fibonacci sequence is given, F₂ = F₁ + F₀ = 1 + 0 = 1. The Fibonacci sequence goes like 0, 1, 1, and so on.

Solved Example:

Find the Fibonacci numbers for F₀ = 2, and F₁ = 6 for 5 terms?

Solution:

Given: N = 5 terms,  F₀ = 2, F₁ = 6

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

F₂ = F_(2-1) + F_(2-2) = F₁ + F₀ = 6 + 2 = 8

F₃ = F_(3-1) + F_(3-2) = F₂ + F₁ = 8 + 6 = 14

F₄ = F_(4-1) + F_(4-2) = F₃ + F₂ = 14 + 8 = 22

F₅ = F_(5-1) + F_(5-2) = F₄ + F₃ = 22 + 14 = 36

Therefore, the Fibonacci series         

 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, F₀ = 3 and F₁ = 8

b)  Number of terms = 15, F₀ = 5 and F₁ = 11