# Fibonacci Numbers

In Maths, the Fibonacci numbers are the numbers ordered in a distinct Fibonacci sequence. These numbers were introduced to represent the positive numbers in a sequence, which follows a defined pattern. The list of the numbers in Fibonacci series is represented by the recurrence relation: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ……..,∞.

## Fibonacci Numbers Definition

The sequence of Fibonacci numbers can be defined as:

 Fn = Fn-1 + Fn-2

Where, Fn is the nth term or number

Fn-1 is the (n-1)th term

Fn-2 is the (n-2)th term

From the equation, we can summarise the definition as, the next number in the sequence, is the sum of the previous two numbers present in the sequence, starting from 0 and 1. Let us create a table to find the next term of Fibonacci sequence, using the formula.

 Fn-1 Fn-2 Fn 0 1 1 1 1 2 1 2 3 2 3 5 3 5 8 5 8 13 8 13 21 13 21 34 21 34 55 34 55 89

In the above table, you can see the numbers in each column are relational and diagonally the numbers are the same in all the three columns.

### Fibonacci Numbers List

The list of numbers of Fibonacci Sequence is given below. This list is formed by using the formula, which is mentioned in the above definition.

 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811,………..

### Fibonacci Numbers Examples

Question 1: Write the first 6 Fibonacci numbers starting from 0 and 1.

Solution: As we know, the formula for Fibonacci sequence is;

Fn = Fn-1 + Fn-2

Since the first term and second term are known to us, i.e. 0 and 1. Thus,

F0 = 0 and F1 = 1

Hence,

Third term, F2 = F0 + F1 = 0+1 = 1

Fourth term, F3 = F2+F1 = 1 + 1 = 2

Fifth term, F4 = F3+F2 = 1+2 = 3

Sixth term, F5 = F4+F3 = 3 + 2 = 5

So, the first six terms of Fibonacci sequence is 0,1,1,2,3,5.

Question 2: Find the next term of Fibonacci series: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34.

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

Therefore, the required term is;

21 + 34 = 55.