Java Program To Find Sum of N Natural Numbers (for Loop, while Loop and Using Arthimetic Formulae)

1. Introduction

In this programming tutorial, You'll learn to a java program to find the sum of n first natural numbers. The positive integers 1, 2, 3, 4, etc. are known as natural numbers and these series must start with digit 1. Here we will show you 4 programs.

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A) Java program to Sum of first 100 natural numbers using for loop
B) Java program to Sum of first 100 natural numbers using while loop
C) Java program to calculate the sum of n natural numbers which input taken from the user
D) Simple Java program to calculate som of natural numbers using arithmetic formula.
.

we have already published in-depth articles on for loop and while loop. Please go through the below articles before seeing the program now.

For Loop in Java
While Loop in Java

2) Java program to Sum of first 100 natural numbers using for loop

This is a simple program running for loop from index 1 to till 100. In each iteration, will add the current index to the previous index. In the first iteration index 1 is added with value '0'. Finally, variable naturalNumbersSum stores the sum of 100 numbers.

package com.java.w3schools.blog.java.program.to;

/**
 * 
 * Java program to Sum of first 100 natural numbers using for loop
 * 
 * @author venkatesh
 *
 */
public class SumOfNaturalNumbersForLoop {

 public static void main(String[] args) {

  int n = 100;

  int naturalNumbersSum = 0;

  for (int index = 1; index <= n; index++) {
   naturalNumbersSum += index;
  }

  System.out.println("For Loop: Sum of frist 100 numbers: " + naturalNumbersSum);
 }

}

Output:

For Loop: Sum of frist 100 numbers: 5050

3) Java program to Sum of first 100 natural numbers using while loop

The below program is implemented using a while loop and works similar to the above for loop.

package com.java.w3schools.blog.java.program.to;

/**
 * 
 * Java program to Sum of first 100 natural numbers using while loop
 * 
 * @author venkatesh
 *
 */
public class SumOfNaturalNumbersWhileLoop {

 public static void main(String[] args) {

  int n = 100;

  int naturalNumbersSum = 0;

  int index = 1;

  while (index <= n) {
   naturalNumbersSum += index;
   index++;
  }
  System.out.println("While Loop: Sum of frist 100 numbers: " + naturalNumbersSum);
 }

}

Output:

While Loop: Sum of frist 100 numbers: 5050

Read more on java program to add two numbers without using '+' operator.

4) Java program to calculate the sum of n natural numbers which input taken from the user

Here we read the input from the user using Scanner class. Scanner has a method nextInt() whick takes the values from the user keyboard.

package com.java.w3schools.blog.java.program.to;

import java.util.Scanner;

/**
 * 
 * Java program to calculate the Sum of first n natural numbers. where n is taken from the user.
 * 
 * @author venkatesh
 *
 */
public class SumOfNaturalNumbersScanner {

 public static void main(String[] args) {

  System.out.println("Enter n value: ");
  Scanner sc = new Scanner(System.in);
  int n = sc.nextInt();

  int naturalNumbersSum = 0;

  int index = 1;

  while (index <= n) {
   naturalNumbersSum += index;
   index++;
  }
  System.out.println("Fom User Input using for loop: Sum of frist 100 numbers: " + naturalNumbersSum);
 }

}

Output:

Enter n value: 1000
Fom User Input using for loop: Sum of frist 100 numbers: 500500

As now, shown 3 programs to calculate the sum but all take time complexity O(n) which is quite good for smaller n value and but if we need to find the sum for 10000089 value then it needs lots of time to execute and run the loop.

5) Simple Java program to calculate som of natural numbers using arithmetic formula

This approach takes completely no time to execute for small and big value for n. The below program is implemented using a super known arithmetic formula. You must have studied at your school. At that time you might not worried about this. But now this will greatly useful for us.

Formula is for sum of frist n natural numbers: n * (n + 1) / 2

Read more on Formula reference

package com.java.w3schools.blog.java.program.to;

import java.util.Scanner;

/**
 * 
 * Java program to calculate the Sum of first n natural numbers using arithmetic
 * formula
 * 
 * @author venkatesh
 *
 */
public class SumOfNaturalNumbersFormula {

 public static void main(String[] args) {

  System.out.println("Enter n value: ");
  Scanner sc = new Scanner(System.in);
  int n = sc.nextInt();

  int naturalNumbersSum = n * (n + 1) / 2;

  System.out.println("Using arthemetic formula: Sum of frist 100 numbers: " + naturalNumbersSum);
 }

}

Output:

Enter n value: 10000089
While Loop: Sum of frist 100 numbers: 1033227621

This program needs not to be run the loop for n times because we have not used any loop concept but directly used a formula. So, the time complexity is reduced to O(1).

6. Conclusion

In this article, we have learned all possible ways to find the sum of natural numbers using for loop, while loop and using formula. And also reading the input from the user. Usage of any loop results in O(n) whereas gives the best results using arithmetic formula O(1).