Java Program to Calculate Sum of First N Natural Numbers
Last Updated :
12 Jan, 2024
In this article, we will check How to calculate the sum of N natural numbers using an iterative approach i.e. using a for a loop and Mathematical Formulae.
Example to Find Sum of N Natural Numbers:
Input: N = 10
Output: Sum of first 10 Natural Number = 55
Input: N = 5
Output: Sum of first 5 Natural Number = 15
Methods to Find the Sum of N Natural Numbers in Java
There are two methods to find the sum of N Natural Numbers as mentioned below:
- Using Loops
- Using Mathematical Formulae
1. Using Loop
Using Loop is one of the most logical methods to find the sum of N natural numbers as we need to just iterate from 1 to N numbers to get the sum. Let us check the approach to implementing the Method.
Note: In this method, we are using for loop but you can use while, do-while too. For loop has three parameters initialization, testing condition, and increment/decrement.
Approach
- Start for loop initialization with i = 1.
- Write the testing condition as i <= N.
- Add increment statement as i++ or i+=1.
- Initialize a variable sum with 0.
- Start adding i with the sum at each iteration of for loop.
- Print sum at the end for loop.
Below is the implementation of above approach:
Java
import java.io.*;
class GFG {
public static void main(String[] args)
{
int N = 10 ;
int sum = 0 ;
System.out.println( "Finding Sum of " + N + " numbers using for loop" );
for ( int i = 1 ; i <= N; i++) {
sum += i;
}
System.out.println( "Sum of first " + N
+ " Natural Number = " + sum);
}
}
|
Output
Finding Sum of 10 numbers using for loop
Sum of first 10 Natural Number = 55
Complexity of the above method:
Time Complexity: O(n)
Auxiliary Space: O(1) because constant space for variables is being used
2. Using Mathematical Formulae
Maths and it’s application is all we need to find the sum of Numbers. Let us check the Formulae and the approach before checking on the Program.
Mathematical Formulae:
Sum = N*(N+1)/2
Approach
- Start for loop initialization with i = 1.
- Write testing condition as i <= N.
- Add increment statement as i++ or i+=1.
- Start Printing i for each iteration.
- Print sum using first N natural number formula.
Below is the implementation of the above approach:
Java
import java.io.*;
class GFG {
public static void main(String[] args)
{
int N = 5 ;
System.out.println( "Finding Sum of " + N + " Numbers using Mathematical Formulae" );
int sum = (N*(N+ 1 ))/ 2 ;
System.out.println( "Sum of first " + N
+ " Natural Number = " + sum);
}
}
|
Output
Finding Sum of 5 Numbers using Mathematical Formulae
Sum of first 5 Natural Number = 15
Complexity of the above method:
Time Complexity: O(1) for Finding the Sum of elements
Auxiliary Space: O(1) as it is using constant space for variables
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