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

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

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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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