Job Updates
Interviews
Connect
Connect & get Notified

Sum of First N Natural numbers

Natural Number Sum

Definition & Explanation

Program to calculate the sum of the first N natural numbers. Natural numbers, also known as counting numbers, are used to represent the quantity of real physical objects. They commence from 1 and extend infinitely.

Example:
Input: N = 5
Output: Sum of the first 5 natural numbers is 15

Approaches to Find the Sum of First N Natural Numbers:

Method 1: Iterative Way

  • Use a loop to iterate from 1 to N and accumulate the sum.

Method 2: Direct Formula

  • Utilize the formula for the sum of the first N natural numbers: ( \text{Sum} = \frac{N \times (N + 1)}{2} ).

Method 3: Recursive Approach

  • Define a recursive function to calculate the sum by adding the current number to the sum of the previous numbers until reaching N.
C

Method 1 :  Iterative way

#include <stdio.h>

int main() {
    // Input: Get the value of N from the user.
    int n;
    scanf("%d", &n);

    // Initialize sum to 0.
    int sum = 0;

    // Iterate from 1 to N and accumulate the sum.
    for (int i = 1; i <= n; i++) {
        // Equivalent to sum = sum + i.
        sum += i;
    }

    // Output: Print the calculated sum.
    printf("Sum is %d", sum);

    return 0;
}

// Time complexity: O(n) - linear time
// Space complexity: O(1) - constant space

Output :

7
Sum is 28

Method 2 : Direct Formula

#include <stdio.h>

int main() {
    // Input: Get the value of N from the user.
    int n;
    scanf("%d", &n);

    // Direct formula to calculate the sum of the first N natural numbers.
    int sum = n * (n + 1) / 2;

    // Output: Print the calculated sum.
    printf("The sum is %d", sum);

    return 0;
}

// Time complexity: O(1) - constant time
// Space complexity: O(1) - constant space

Output :

7
The sum is 28

Method 3 :  Recursive Approach

#include <stdio.h>

// Recursive function to calculate the sum of the first N natural numbers.
int getSum(int sum, int n) {
    if (n == 0) 
        return sum;
    
    return n + getSum(sum, n - 1);
}

int main() {
    // Input: Get the value of N from the user.
    int n, sum = 0;
    scanf("%d", &n);

    // Output: Print the calculated sum using the recursive function.
    printf("%d", getSum(sum, n));

    return 0;
}

// Time complexity: O(n) - linear time
// Space complexity: O(1) - constant space
// Auxiliary space complexity: O(N) - due to function call stack

Output :

Enter the value of N: 7
28
C++

Method 1 :  Iterative way

#include <iostream>

int main() {
    // Input: Get the value of N from the user.
    int n;
    std::cin >> n;

    // Initialize sum to 0.
    int sum = 0;

    // Iterate from 1 to N and accumulate the sum.
    for (int i = 1; i <= n; i++) {
        // Equivalent to sum = sum + i.
        sum += i;
    }

    // Output: Print the calculated sum.
    std::cout << "Sum is " << sum;

    return 0;
}

// Time complexity: O(n) - linear time
// Space complexity: O(1) - constant space

Output :

Enter the value of N: 7
Sum is 28

Method 2: Direct Formula (C++)

#include <iostream>

int main() {
    // Input: Get the value of N from the user.
    int n;
    std::cin >> n;

    // Direct formula to calculate the sum of the first N natural numbers.
    int sum = n * (n + 1) / 2;

    // Output: Print the calculated sum.
    std::cout << "The sum is " << sum;

    return 0;
}

// Time complexity: O(1) - constant time
// Space complexity: O(1) - constant space

Output :

Enter the value of N: 7
Sum is 28

Method 3: Recursive Approach (C++)

#include <iostream>

// Recursive function to calculate the sum of the first N natural numbers.
int getSum(int sum, int n) {
    if (n == 0) 
        return sum;
    
    return n + getSum(sum, n - 1);
}

int main() {
    // Input: Get the value of N from the user.
    int n;
    std::cin >> n;

    // Output: Print the calculated sum using the recursive function.
    std::cout << getSum(0, n);

    return 0;
}

// Time complexity: O(n) - linear time
// Space complexity: O(1) - constant space
// Auxiliary space complexity: O(N) - due to function call stack

Output :

Enter the value of N: 7
Sum is 28
JAVA

Method 1: Iterative Way (Java)

import java.util.Scanner;

public class SumIterative {
    public static void main(String[] args) {
        // Input: Get the value of N from the user.
        Scanner scanner = new Scanner(System.in);
        System.out.print("Enter the value of N: ");
        int n = scanner.nextInt();

        // Initialize sum to 0.
        int sum = 0;

        // Iterate from 1 to N and accumulate the sum.
        for (int i = 1; i <= n; i++) {
            // Equivalent to sum = sum + i.
            sum += i;
        }

        // Output: Print the calculated sum.
        System.out.println("Sum is " + sum);
    }
}

Output :

Enter the value of N: 7
Sum is 28

Method 2: Direct Formula (Java)

import java.util.Scanner;

public class SumDirectFormula {
    public static void main(String[] args) {
        // Input: Get the value of N from the user.
        Scanner scanner = new Scanner(System.in);
        System.out.print("Enter the value of N: ");
        int n = scanner.nextInt();

        // Direct formula to calculate the sum of the first N natural numbers.
        int sum = n * (n + 1) / 2;

        // Output: Print the calculated sum.
        System.out.println("The sum is " + sum);
    }
}

Output :

Enter the value of N: 7
Sum is 28

Method 3: Recursive Approach (Java)

import java.util.Scanner;

public class SumRecursive {
    // Recursive function to calculate the sum of the first N natural numbers.
    public static int getSum(int sum, int n) {
        if (n == 0) 
            return sum;
        
        return n + getSum(sum, n - 1);
    }

    public static void main(String[] args) {
        // Input: Get the value of N from the user.
        Scanner scanner = new Scanner(System.in);
        System.out.print("Enter the value of N: ");
        int n = scanner.nextInt();

        // Output: Print the calculated sum using the recursive function.
        System.out.println(getSum(0, n));
    }
}

Output :

Enter the value of N: 7
Sum is 28
Python

Method 1: Iterative Way (Python)

# Input: Get the value of N from the user.
n = int(input("Enter the value of N: "))

# Initialize sum to 0.
sum_val = 0

# Iterate from 1 to N and accumulate the sum.
for i in range(1, n+1):
    # Equivalent to sum = sum + i.
    sum_val += i

# Output: Print the calculated sum.
print("Sum is", sum_val)

Output :

Enter the value of N: 7
Sum is 28

Method 2: Direct Formula (Python)

# Input: Get the value of N from the user.
n = int(input("Enter the value of N: "))

# Direct formula to calculate the sum of the first N natural numbers.
sum_val = n * (n + 1) // 2

# Output: Print the calculated sum.
print("The sum is", sum_val)

Output :

Enter the value of N: 7
Sum is 28

Method 3: Recursive Approach (Python)

# Recursive function to calculate the sum of the first N natural numbers.
def get_sum(sum_val, n):
    if n == 0:
        return sum_val
    
    return n + get_sum(sum_val, n - 1)

# Input: Get the value of N from the user.
n = int(input("Enter the value of N: "))

# Output: Print the calculated sum using the recursive function.
print(get_sum(0, n))

Output :

Enter the value of N: 7
Sum is 28
View All Codes