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# Fibonacci Numbers

In mathematics, Fibonacci series is one type of number series. Number series is nothing but the sequence of number formed under certain condition. There are many types of number series. The subsequence number is the sum of two previous numbers. The first two numbers of Fibonacci series is 0 and 1. The formula to form the Fibonacci series is F_n = F_(n-1) + F_(n-2) .

Where,

F_0 = 0 and F_1 = 1

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## What are Fibonacci Numbers?

The fibonacci numbers are the sequence of the numbers where any particular number will be the sum of the previous two numbers in the series. This is described by the formula,

Fn = Fn-1 + Fn-2

## Fibonacci Number Sequence

The starting two digits of the fibonacci series are 0 and 1. And from the third digit the series expands using the rule described above. The first 15 digits of the fibonacci series are,

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610…

The ratio of the fibonacci series becomes a constant after 15 numbers in the series and is correct to 10 decimal places and is the value for phi called as the golden ratio. The golden ratio is,

1.6180339887…

The phi value or the golden ratio can be used to find the nth digit in the fibonacci series. The position value of 0 is 0. And the nth number in the fibonacci series is found by substituting the values in the formula below and rounding the result to the nearest whole value. The formula for calculating the nth fibonacci number is,

[F_n = (Phi ^n) / sqrt5]

## Fibonacci Numbers List

Fibonacci series is one of the most interesting sequence of numbers which series starts with 0, 1 and goes on based on a simple rule. Any number in the Fibonacci series is the sum of the previous two numbers in the fibonacci series. And the fibonacci series goes on by this rule.

Below you could see the list of Fibonacci numbers,

## Fibonacci Numbers Examples

Here are the Examples on Fibonacci Sequence

### Solved Examples

Question 1: Find the first three Fibonacci numbers.
Solution:
Formula to form the Fibonacci series:

Fibonacci series F_(n) = F_(n-1) + F_(n-2)

Where,

F_0 = 0 and F_1 = 1

The Fibonacci series up to three number: 0 1 1

Question 2: Find the first five Fibonacci numbers.
Solution:
Formula to form the Fibonacci sequence list:

Fibonacci series F_(n) = F_(n-1) + F_(n-2)

Where,

F_0 = 0 and F_1 = 1

The Fibonacci series up to five number: 0 1 1 2 3

Question 3: Find the first thirteen Fibonacci numbers.
Solution:
Formula to form the Fibonacci series:

Fibonacci series F_(n) = F_(n-1) + F_(n-2)

Where,

F_0 = 0 and F_1 = 1

The Fibonacci series up to thirteen number: 0 1 1 2 3 5 8 13 21 34 55 89

Question 4: Find the value of 17th number in Fibonacci series.
Solution:
Formula to form the Fibonacci series:

Fibonacci series F_(n) = F_(n-1) + F_(n-2)

Where,

F_0 = 0 and F_1 = 1

The Fibonacci series up to seventeen number: 0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 The 17th value of Fibonacci series is 987

Question 5: Find the value of 19th number in Fibonacci series.
Solution:
Formula to form the Fibonacci series:

Fibonacci series F_(n) = F_(n-1) + F_(n-2)

Where,

F_0 = 0 and F_1 = 1

The Fibonacci series up to nineteen number: 0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 The 19th value of Fibonacci series is 610.

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