Java Program to Find the Sum of First N Odd & Even Numbers

In Java, numbers that are divisible by 2 are called even numbers (ending with 0, 2, 4, 6, 8), while numbers that are not divisible by 2 are called odd numbers (ending with 1, 3, 5, 7, 9).

In this article, we will learn how to calculate the sum of the first N even numbers and the first N odd numbers using two simple approaches.

Example:

Input : 8
Output:

Sum of First 8 Even numbers = 72
Sum of First 8 Odd numbers = 64

Approach 1: Iterative Method

class GFG {
    public static void main(String[] args) {
        int n = 8;
        int evenSum = 0;
        int oddSum = 0;
        for (int i = 1; i <= 2 * n; i++) {
            if ((i & 1) == 0)
                evenSum += i;
            else
                oddSum += i;
        }
        System.out.println("Sum of First " + n + " Even numbers = " + evenSum);
        System.out.println("Sum of First " + n + " Odd numbers = " + oddSum);
    }
}

Explanation:

• The variable n defines how many even and odd numbers are needed.
• A loop runs from 1 to 2*n to cover both odd and even numbers.
• The bitwise AND operator & is used to check whether a number is even or odd.
• Even numbers are added to evenSum and odd numbers to oddSum.
• Time Complexity: O(N) and Auxiliary Space: O(1)

Approach 2: Using Arithmetic Progression (AP) Formulas

Mathematical Formulas

• Sum of first N even numbers: N × (N + 1)
• Sum of first N odd numbers: N × N

class GFG {
    static int sumOfEvenNums(int n) {
        return n * (n + 1);
    }
    static int sumOfOddNums(int n) {
        return n * n;
    }

    public static void main(String[] args) {
        int n = 10;
        int evenSum = sumOfEvenNums(n);
        int oddSum = sumOfOddNums(n);
        System.out.println("Sum of First " + n + " Even numbers = " + evenSum);
        System.out.println("Sum of First " + n + " Odd numbers = " + oddSum);
    }
}

Sum of First 10 Even numbers = 110
Sum of First 10 Odd numbers = 100

Explanation:

• Two helper methods are defined to compute sums using formulas instead of loops.
• Time Complexity: O(1) and Auxiliary Space: O(1)