JavaScript Program to print Fibonacci Series

09 Jul, 2022
Suppose in a Class, the Teacher asked students of roll number 1 to write 0 and roll number 2 to write 1 on the blackboard and asked for the rest of the students, to write the summation of your previous two students’. The series written on the board will look like 0,1,1,2,3,5,8,..........
The teacher then told the students, this series is known as the Fibonacci series. It can be represented by the below equation
 Fn = Fn-1 + Fn-2
Where F0=1 and F1=1. The Fibonacci numbers are the numbers in the following integer sequence 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ........In mathematical terms, the sequence Fn of Fibonacci numbers is defined by the recurrence relation
Fn = Fn-1 + Fn-2 with seed values F0 = 0 and F1 = 1
Examples: 
Input : 5 
Output : 8

Input :8
Output :34

As the first Fibonacci number is 0 and the second is 1. Also, we know that the nth Fibonacci number is the summation of n-1 and n-2 term.So, to get the nth Fibonacci term we can followfib(1)=0fib(2)=1fib(3)=fib(2)+fib(1)fib(4)=fib(3)+fib(2)....fib(n)=fib(n-1)+fib(n-2)
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Example: By using for loop
javascript
<script type = "text/javascript">function fibonacci(num){    var num1=0;    var num2=1;    var sum;    var i=0;    for (i = 0; i < num; i++)     {        sum=num1+num2;        num1=num2;        num2=sum;    }    return num2;}  document.write("Fibonacci(5): "+fibonacci(5)+"<br>");document.write("Fibonacci(8): "+fibonacci(8)+"<br>");</script>
Output:
Fibonacci(5): 3
Fibonacci(8): 13
Example: By using while loop 
javascript
<script type = "text/javascript">function fibonacci(num)    {        if(num==1)            return 0;        if(num==2)            return 1;        var num1=0;        var num2=1;        var sum;        var i=2;        while (i<num)          {            sum=num1+num2;            num1=num2;            num2=sum;            i+=1;        }        return num2;    }  document.write("Fibonacci(5): "+fibonacci(5)+"<br>");document.write("Fibonacci(8): "+fibonacci(8)+"<br>");</script>
Output:
Fibonacci(5): 3
Fibonacci(8): 13
By using recursion: As we know that the nth Fibonacci number is the summation of n-1 and n-2 term and the n-1 term is the summation of n-2 and n-3 term.So, to get the nth Fibonacci term we can followfib(n)=fib(n-1)+fib(n-2)fib(n)=fib(n-2)+fib(n-3)+fib(n-3)+fib(n-4)....fib(n)=fib(1)+fib(0)+fib(1)+fib(0)+fib(1)+fib(0)....fib(1)+fib(0) [terms containing sum of fib(1) and fib(0)fib(1)=0fib(2)=1
Example:
javascript
<script type = "text/javascript">function fibonacci(num)    {           if(num==1)            return 0;        if (num == 2)            return 1;        return fibonacci(num - 1) + fibonacci(num - 2);    }document.write("Fibonacci(5): "+fibonacci(5)+"<br>");document.write("Fibonacci(8): "+fibonacci(8)+"<br>");</script>
Output:
Fibonacci(5): 3
Fibonacci(8): 13
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