In this article we are going to see find sum of Arithmetic Progression using Java programming language.

## Java Program to Find Sum of Arithmetic Progression

The formula to calculate the sum of arithmetic progression is

Sn=n/2(2a+(n-1)d)

where,

- a = first number the AP
- n = number of terms in the AP
- d = common difference between elements

**Example:**

In an AP if the first term i.e., a = 2, total number of terms i.e., n = 6 and the common difference between the terms i.e., d = 3, then

S

_{n}

=n/2(2a+(n-1)d) =6/2 (2 X 2 + (6-1) X 3) =3(4+15) = 3 X 19 = 57

We can also obtain the nth term of an AP series by using the formula

T

_{n}

= a + (n – 1) d

Let’s see different ways to find sum of Arithmetic Progression.

- By Using User Input Value and Using the Formula
- By Using User Input Value Without Using the Sum Formula

### Method-1: Java Program to Find Sum of Arithmetic Progression Using User Input Value Using the Formula

**Approach:**

- Take the user input for the first term, common difference, and the number of terms.
- Use the formula to get the sum of the series and print the result

**Program:**

import java.util.Scanner; public class Main { public static void main(String[] args) { Scanner sc = new Scanner(System.in); System.out.print("Enter the first term of the series: "); int a = sc.nextInt(); System.out.print("Enter the common difference of the series: "); int d = sc.nextInt(); System.out.print("Enter the number of terms in the series: "); int n = sc.nextInt(); int sum = (n * (2 * a + (n - 1) * d)) / 2; int tn = a + (n - 1) * d; System.out.println("The sum of the series is: "); for (int i = a; i <= tn; i += d) { if (i != tn) System.out.printf("%d + ", i); else System.out.printf("%d = %d", i, sum); } } }

Output: Enter the first term of the series: 40 Enter the common difference of the series: 4 Enter the number of terms in the series: 15 The sum of the series is: 40 + 44 + 48 + 52 + 56 + 60 + 64 + 68 + 72 + 76 + 80 + 84 + 88 + 92 + 96 = 1020

### Method-2: Java Program to Find Sum of Arithmetic Progression By Using User Input Value Without Using the Sum Formula

**Approach:**

- Take the user input for the first term, common difference, and the number of terms.
- Initialize sum variable as 0.
- Use a for loop for i = 0 -> n.
- Inside the for loop update the sum variable as sum += a + i * d
- Return sum.
- Print the result.

**Program:**

import java.util.Scanner; public class Main { public static void main(String[] args) { Scanner sc = new Scanner(System.in); System.out.print("Enter the first term of the series: "); int a = sc.nextInt(); System.out.print("Enter the common difference of the series: "); int d = sc.nextInt(); System.out.print("Enter the number of terms in the series: "); int n = sc.nextInt(); System.out.println("The sum of the series is: " + calcSum(a, d, n)); } private static int calcSum(int a, int d, int n) { int sum = 0; for (int i = 0; i < n; i++) { sum += a + i * d; } return sum; } }

Output: Enter the first term of the series: 40 Enter the common difference of the series: 4 Enter the number of terms in the series: 15 The sum of the series is: 1020

Interested in programming and want to excel in it by choosing the short ways. Then, practicing with the available Java Program list is mandatory.