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How to find the nth term of the Fibonacci series using recursion

Buchiredddypalli Koushik

Fibonacci series

Let’s first see what the Fibonacci series is:

The Fibonacci series generally starts with 1 and 1 as default, which means that the first and second term is always 1.

The series looks like this:

1,1,2,3,5,8,13...

We can see that the first and the second term is one, and the succeeding term is calculated by the addition of the previous two terms.

So to get the sequence, we need to add the previous two elements. The sequence will be generated in the same way throughout the process.

In this shot, we’ll implement the Fibonacci series using recursion.

Note: Recursion is the process in which the function calls itself. We use recursion here to implement the nthn^{th} term of the Fibonacci series.

Example

The 1st term of the Fibonacci series is 1.

  • Here n is 1 so if n==1||n==2 we return the value 1.

The 5th term of the Fibonacci series is 5.

  • Here, n is 5, so we call fib(n-1)+fib(n-2) recursively to get the value 5.

Algorithm

  • If n is 0, then return 0.

  • If n is 1 or 2, we return 1.

  • Otherwise, we use fib(n-1)+fib(n-2), which will be called recursively throughout the process.

Pseudocode

if(n==0 or n==1) 

{
return 1 
}

return fib(n-1)+fib(n-2);
%0 node_1 fib(5) node_2 fib(4) node_1->node_2 node_3 fib(3) node_1->node_3 node_1647646200620 fib(3) node_2->node_1647646200620 node_1647646207286 fib(2) node_2->node_1647646207286 node_1647646294531 fib(2) node_1647646200620->node_1647646294531 node_1647646259136 fib(1) node_1647646200620->node_1647646259136 node_1647646345598 fib(1) node_1647646294531->node_1647646345598 node_1647646354838 fib(0) node_1647646294531->node_1647646354838 node_1647646440757 fib(1) node_1647646207286->node_1647646440757 node_1647646450877 fib(0) node_1647646207286->node_1647646450877 node_1647646376379 fib(2) node_3->node_1647646376379 node_1647646378109 fib(1) node_3->node_1647646378109 node_1647646390474 fib(1) node_1647646376379->node_1647646390474 node_1647646387804 fib(0) node_1647646376379->node_1647646387804
Recursive tree to calculate Fibonacci of 5
#include<stdio.h>
int fib(int); // Function declaration
int main()
{
	int n; // Declaration of variable
	scanf("%d",&n);
	printf("The %d term in the fibnoci series is: %d ",n,fib(n)); // Calling function
}
int fib(int n) // Function declaration
{
	if(n==0)
	{
		return 0;
	}
	if(n==1||n==2)
	{
		return 1;
	}
	return fib(n-1)+fib(n-2); // Recursive funnction
}

Enter the input below

nth term of Fibonacci Series

Explanation

First, we read the value of n.

  • Line 2: We declare int fib(int).

  • Line 7: We call the function fib(n).

  • Line 9: We declare the function.

  • Line 11–14: If n is 0, we return 0.

  • Line 15–18: If n is 1 or 2, we return 1.

  • Line 19: If n is something other than 0, 1, or 2 then we call fib(n-1)+fib(n-2) recursively.

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recursion
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c

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Buchiredddypalli Koushik
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