Java – Find Sum of First N Natural Numbers

To find the sum of first N natural numbers, you can either use direct formula or use a looping technique to traverse from 1 to to N and compute the sum.

sum = 1 + 2 + 3 + . . + n

In this tutorial, we shall start with Java programs using looping statements to compute the sum. Then we shall go through a Java program that uses formula to find the sum. At last, we shall look into recursion technique to find the sum.

Algorithm

Following algorithm can be used to find the sum of first N natural numbers using Java looping statements.

  1. Start.
  2. Read n.
  3. Initialize sum with 0.
  4. Initialize i with 0.
  5. Check if i is less than or equal to n. If false go to step 8.
  6. Add i to sum.
  7. Increment i. Go to step 5.
  8. Print the sum.
  9. Stop.

Find Sum of First N Natural Numbers using While Loop

In the following Java program, we use Java While Loop to implement the algorithm to find sum of first N natural numbers.

Example.java

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/**
 * Java Program - Sum of First N Natural Numbers
 */

public class Example {

	public static void main(String[] args) {
		int n = 10;
		int sum=0;
		
		int i=1;
		while (i<=n) {
			sum += i;
			i++;
		}
			
		System.out.println(sum);
	}
	
}

Output

55

Find Sum of First N Natural Numbers using For Loop

In the following Java program, we use Java For Loop to implement the algorithm to find sum of first N natural numbers.

Example.java

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/**
 * Java Program - Sum of First N Natural Numbers
 */

public class Example {

	public static void main(String[] args) {
		int n = 10;
		int sum=0;
		
		for(int i=1; i<=n; i++)
			sum += i;
			
		System.out.println(sum);
	}
	
}

Output

55

Find Sum of First N Natural Numbers using Formula

Formula to find the sum of first n Natural Numbers is n*(n+1)/2. In the following Java program, we shall use this formula.

Example.java

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/**
 * Java Program - Sum of First N Natural Numbers
 */

public class Example {

	public static void main(String[] args) {
		int n = 10;
		int sum = (n * (n + 1)) / 2;
			
		System.out.println(sum);
	}
	
}

Output

55

Find Sum of First N Natural Numbers using Recursion

We can also use recursion function to find the sum of first N natural numbers.

Example.java

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/**
 * Java Program - Sum of First N Natural Numbers
 */

public class Example {

	public static void main(String[] args) {
		int n = 10;
		int sum = sumOfN(n);
		System.out.println(sum);
	}
	
	static int sumOfN(int n) {
		if (n == 1)
			return 1;
		else
			return n + sumOfN(n-1);
	}
}

Output

55

Conclusion

In this Java Tutorial, we learned how to compute the sum of first n natural numbers with the help of different techniques in Java.