Java Program to Print the Series 1 2 6 15 31 … N

In the previous article we have discussed about Java Program to print Series 1 3 6 11 18 … N

In this article we are going to see how to print the series 1 2 6 15 31 … N by using Java programming language.

Java Program to Print the Series 1 2 6 15 31 … N

On observing the pattern carefully, we can see

1^st number starts from 1 which is at index 0.

Then the next number is addition of previous number with square of the index, where index starts from 0 and goes on up to n.

Example:

+1^2 +2^2 +3^2 +4^2 +5^2 +(N-1)^2

Let’s see different ways to print the series 1 2 6 15 31 … N

By Using For Loop
By Using while Loop
By Using User Defined Method

Method-1: Java Program to Print the Series 1 2 6 15 31 … N By Using For Loop

Approach:

Create Scanner class object.
Declare an integer variable say ‘n’ which holds the Nth term of the series.
Prompt the user to enter a number as value of n.
Let declare an integer variable say ‘result’ and initialize it to 1.
Use a for loop from i=1 to i<=n-1 where the loop is incremented by 1
Inside the for loop we will find the value of result+=i*i.
Print the result in the series.

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 Nth term “N” ");
        int n = s.nextInt();
        int result = 1;
        System.out.print(result);
        //for loop to print the series
        for (int i = 1; i <= n-1; i++) 
        {
            result +=i*i; 
            System.out.print(" "+result);
        } 
    }
}

Output:

Enter the Nth term “N” 
5
1 2 6 15 31

Method-2: Java Program to Print the Series 1 2 6 15 31 … N By Using While Loop

Approach:

Create Scanner class object.
Declare an integer variable say ‘n’ which holds the Nth term of the series.
Prompt the user to enter a number as value of n.
Let declare an integer variable say ‘result’ and initialize it to 1
Declare and initialize an integer variable i=1
Continue a while loop till i<=n-1, where i is incremented by 1.
Inside while loop find the value of result += i*i
Print the result in the series.

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 Nth term “N” ");
        int n = s.nextInt();
        int result=1;
        System.out.print(result);
        int i=1;
        while(i<=n-1)
        {
            result +=i*i; 
            System.out.print("  "+result);
            i++;
        }      
    }
}

Output:

Enter the Nth term “N” 
7
1 2 6 15 31 56 92

Method-3: Java Program to Print the Series 1 2 6 15 31 … N By Using User Defined Method

Approach:

Create Scanner class object.
Declare an integer variable say ‘n’ which holds the Nth term of the series.
Prompt the user to enter a number as value of n.
Call a user defined method printSeries() by passing n as parameter.
Inside method declare an integer variable say ‘result’ and initialize it to 1.
Use a for loop from i=1 to i<=n-1 where the loop is incremented by 1
Inside the for loop we will find the value of result+=i*i.
Print the result in the series.

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 Nth term 'N' ");
        int n = s.nextInt();
        // calling printSeries method to print the series
        printSeries(n);
    }
    
    //printSeries metthod to print the series
    public static void printSeries(int n)
    {
        int result = 1;
        System.out.print(result);
        //for loop to print the series
        for (int i = 1; i <=n-1; i++) 
        {
            result +=i*i; 
            System.out.print(" "+result);
        } 
    }
}

Output:

Enter the value of Nth term 'N' 
9
1 2 6 15 31 56 92 141 205

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