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# Fibonacci Numbers

In mathematics, the Fibonacci numbers are the numbers arranged in a particular sequence. The Fibonacci numbers provide the base of an interesting way to represent positive numbers. The Fibonacci Sequence of the numbers is defined by the recurrence relation: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ........
In short, the sequence of Fibonacci numbers is

$F_n = F_{n-1} + F_{n-2}$

where, $F_n$ is nth term number
$F_{n-1}$ is the (n - 1)th term
$F_{n-2}$ is the (n - 2)th term
From above relation $F_0 = 0$, $F_1 = 1$ and $F_2 = 1$

=> The first three numbers in the Fibonacci sequence are 0, 1, and 1.

Examples of Fibonacci Numbers

Below are the Examples on Fibonacci Sequence

Problem 1: Find the first five Fibonacci numbers.

Solution: Formula to form the Fibonacci sequence : $F_n = F_{n-1} + F_{n-2}$

We know that, first three Fibonacci numbers are 0, 1, 1 and each next term is sum of previous two terms.

So $F_3$ = $F_2$ + $F_1$

= 1 + 1 = 2

and $F_4$ = $F_3$ + $F_2$

= 2 + 1 = 3

First five Fibonacci numbers are: 0, 1, 1, 2, 3.

Problem 2: Find the next term of fibonacci series: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55.

Solution: Each next term of the fibonacci series is sum of previous two terms.

So required term is, 55 + 34 = 89.

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