# Java Program to Find Sum of Arithmetic Progression

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.

### 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.