In the previous article, we have discussed about Java Program to Find the Sum of Series (1*2) + (2*3) + (3*4) + …… + N

In this article we are going to see how to find sum of the series (a*2) + (a*3) + …… + (a*N) by using Java programming language.

## Java Program to Find the Sum of Series (a*2) + (a*3) + (a*4) + …… + (a*N)

On observing the pattern carefully, we can see terms are in the form of `(a*b)`

where ‘`b`

‘ value starts from 2 and in each term it is incremented by 1.

**Example:**

Suppose a = 2 n = 5 Then sum of series: (2*2) + (2*3) + (2*4) + (2*5) = 4+6+8+10 = 28

Let’s see different ways to find sum of the series (a*2) + (a*3) + …… + N.

### Method-1: Java Program to Find the Sum of Series (a*2) + (a*3) + (a*4) + …… + (a*N) By Using For Loop

**Approach:**

- Declare an integer variable say ‘
`a`

’ which holds the value of first “`a`

” which will be fixed. - Declare an integer variable say ‘
`n`

’ which holds the last value of second no in the series. - Create Scanner class object.
- Prompt the user to enter values for
`a`

and`n`

. - Use a for loop
`from i=2 to i<=n`

- Inside for loop we will multiply
`a*i`

and add with sum. - Print the result.

**Program:**

import java.util.*; public class Main { public static void main(String args[]) { //creating object of Scanner class Scanner s = new Scanner(System.in); //Taking input of number of elements in the series System.out.println("Enter the value of a "); int a = s.nextInt(); //Taking input of number of elements in the series System.out.println("Enter the value of last number 'n' "); int n = s.nextInt(); //for loop to print the series long sum = 0; for (int i = 2; i <= n; i++) sum += a * i; System.out.println("Sum of the series is " + sum); } }

Output: Enter the value of a 2 Enter the value of last number 'n' 5 Sum of the series is 28

### Method-2: Java Program to Find the Sum of Series (a*2) + (a*3) + (a*4) + …… + (a*N) By Using While Loop

**Approach:**

- Declare an integer variable say ‘
`a`

’ which holds the value of first “`a`

” which will be fixed. - Declare an integer variable say ‘
`n`

’ which holds the last value of second no in the series. - Create Scanner class object.
- Prompt the user to enter values for
`a`

and`n`

. - Use a while loop
`from i=2 to i<=n`

- Inside while loop we will multiply
`a*i`

and add with sum. - Print the result.

**Program:**

import java.util.*; public class Main { public static void main(String args[]) { //creating object of Scanner class Scanner s = new Scanner(System.in); //Taking input of number of elements in the series System.out.println("Enter the value of a "); int a = s.nextInt(); //Taking input of number of elements in the series System.out.println("Enter the value of last number 'n' "); int n = s.nextInt(); //while loop to print the series double sum = 0; int i = 2; while(i <= n) { sum += a*i; i ++; } System.out.println("sum of the series is " + sum); } }

Output: Enter the value of a 2 Enter the value of last number 'n' 5 sum of the series is 28.0

### Method-3: Java Program to Find the Sum of Series (a*2) + (a*3) + (a*4) + …… + (a*N) By Using User Defined Method

**Approach:**

- Declare an integer variable say ‘
`a`

’ which holds the value of first “`a`

” which will be fixed. - Declare an integer variable say ‘
`n`

’ which holds the last value of second no in the series. - Create Scanner class object.
- Prompt the user to enter value for
`a`

and`n`

. - Then call a user defined method by passing
`a`

and`n`

. - Use a for loop
`from i=2 to i<=n`

- Inside for loop we will multiply
`a*i`

and add with sum. - Print the result.

**Program:**

import java.util.*; public class Main { public static void main(String[] args) { // creating object of scanner class Scanner s = new Scanner(System.in); //Taking input of number of elements in the series System.out.println("Enter the value of a "); int a = s.nextInt(); //Taking input of number of elements in the series System.out.println("Enter the value of last number 'n' "); int n = s.nextInt(); // calling m1 method to print the series m1(a,n); } public static void m1(int a, int n) { //for loop to print the series long sum = 0; for (int i = 2; i <= n; i++) sum += a * i; System.out.println("Sum of the series is " + sum); } }

Output: Enter the value of a 5 Enter the value of last number 'n' 10 Sum of the series is 270

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