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Enter your arbitrary First Term (F0), Second Term (F1) and then the term (n) for which you want to find Fn. Finally press Find Fibonacci Number button.

NOTE:

• This calculator can generate Fibonacci Number up to its 10,000th term (F10,000).
• The first term (F0) and second term (F1) can be positive or negative integers.
F0
F1
n

Result:

This advanced Fibonacci number calculator can accept arbitrary first and second term and provides you the Fibonacci number of the given nth term. You can find Fibonacci number for up to its 10,000th term. So, you do not need to do manual additions or other calculations to find the Fibonacci numbers up to F10,000.

### Using This Calculator

Follow these steps to generate a Fibonacci Number:

1. Enter the First Term (F0) of the Fibonacci Sequence.
2. Enter the Second Term (F1) of the Fibonacci Sequence.
3. Enter the nth term index. This field accepts input up to 10,000.
4. Finally press the Find Fibonacci Number button.
5. The result will be displayed below the button.

#### Example

If you want to find the Fibonacci Number of 100th term (F100) with an arbitrary starter of F0 = 10 and F1 = 20, then enter 10 in the First Term (F0) field, 10 in the Second Term (F1) field and enter 100 in the n field. Finally press the Find Fibonacci Number button.

## Fibonacci Numbers

### Fibonacci Numbers or Fibonacci Sequence

Fibonacci sequence is a series of numbers in mathematics which follows a specific pattern. Fibonacci numbers are denoted by the term Fn. 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.

### Formula For Fibonacci Sequence With arbitrary Starters

The formula used to generate Fibonacci Series Fn is:

Fn = Fn-2 + Fn-1

##### where:

• F0 = a
• F1 = b
• a and b are the arbitrary starters.
• n > 1

#### Using the Formula

1. Let us consider the first term (F0) in the Fibonacci sequence is 10.
2. The second term (F1) in the Fibonacci sequence is 20.
3. To find the remaining terms, you have to apply the formula (Fn = Fn-2 + Fn-1).
4. So, F2 = F0 + F1.
i.e. F2 = 10 + 20 = 30.
5. Likewise, F3 = F1 + F2.
i.e. F3 = 20 + 30 = 50.
6. 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.

### Formula For nth Fibonacci Number

There is a simpler way to find the nth term alone of the Fibonacci sequence using the golden ratio.

The formula used to find the nth term Fn with arbitrary starters is:

Fn = xΦn + yΨn
x = (F1 - F0Ψ) ÷ √5
y = (ΦF0 - F1) ÷ √5

##### where:
• F0 is the first arbitrary term.
• F1 is the second arbitrary term.
• Φ is the golden ratio.
• Φ = (1 + √5) ÷ 2
• Ψ = 1 - Φ = (1 - √5) ÷ 2
• n > 1

## Reference

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