Enter your arbitrary First Term (*F _{0}*), Second Term (

**NOTE:**

- This calculator can generate Fibonacci Number up to its 10,000
^{th}term (*F*)._{10,000} - The first term (
*F*) and second term (_{0}*F*) can be positive or negative integers._{1}

This advanced Fibonacci number calculator can accept arbitrary first and second term and provides you the Fibonacci number of the given n^{th} term. You can find Fibonacci number for up to its 10,000^{th} term. So, you do not need to do manual additions or other calculations to find the Fibonacci numbers up to *F _{10,000}*.

Follow these steps to generate a Fibonacci Number:

- Enter the First Term (
*F*) of the Fibonacci Sequence._{0} - Enter the Second Term (
*F*) of the Fibonacci Sequence._{1} - Enter the n
^{th}term index. This field accepts input up to 10,000. - Finally press the Find Fibonacci Number button.
- The result will be displayed below the button.

If you want to find the Fibonacci Number of 100^{th} term (*F*_{100}) with an arbitrary starter of *F _{0}* = 10 and

Fibonacci sequence is a series of numbers in mathematics which follows a specific pattern. Fibonacci numbers are denoted by the term ** F_{n}**. Every number in the Fibonacci sequence is the sum of the two preceding Fibonacci numbers. Now, let us see the formula used to generate the Fibonacci Sequence.

The formula used to generate Fibonacci Series **F _{n}** is:

*F _{n}* =

*F*= a_{0}*F*= b_{1}**a**and**b**are the arbitrary starters.- n > 1

- Let us consider the first term (
*F*) in the Fibonacci sequence is 10._{0} - The second term (
*F*) in the Fibonacci sequence is 20._{1} - To find the remaining terms, you have to apply the formula (
*F*=_{n}*F*+_{n-2}*F*)._{n-1} - So,
*F*=_{2}*F*+_{0}*F*._{1}

i.e.*F*= 10 + 20 = 30._{2} - Likewise,
*F*=_{3}*F*+_{1}*F*._{2}

i.e.*F*= 20 + 30 = 50._{3} - Thus, the first 10 terms of this Fibonacci series with arbitrary starters are 10, 20, 30, 50, 80, 130, 210, 340, 550, 890,... Use the above calculator to generate more Fibonacci numbers with arbitrary starters.

There is a simpler way to find the n^{th} term alone of the Fibonacci sequence using the golden ratio.

The formula used to find the n^{th} term **F _{n}** with arbitrary starters is:

*F _{n}* = x

x = (

y = (Φ

*F*is the first arbitrary term._{0}*F*is the second arbitrary term._{1}*Φ*is the golden ratio.*Φ*= (1 + √5) ÷ 2*Ψ*= 1 -*Φ*= (1 - √5) ÷ 2- n > 1

- About Fibonacci series in wikipedia.org

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Page Last Modified On:** Apr 22, 2021 **

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