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

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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