Find the nth term of the given series

Given the first two terms of the series as 1 and 6 and all the elements of the series are 2 less than the mean of the number preceding and succeeding it. The task is to print the nth term of the series.
First few terms of the series are:

1, 6, 15, 28, 45, 66, 91, …

Examples:

Input: N = 3
Output: 15

Input: N = 1
Output: 1



Approach: The given series represents odd positioned numbers in the triangular number series. Since the nth triangular number can easily be found by (n * (n + 1) / 2), so for finding the odd numbers we can replace n by (2 * n) – 1 as (2 * n) – 1 will always result in odd numbers i.e. the nth number of the given series will be ((2 * n) – 1) * n.

Below is the implementation of the above approach:

C++

filter_none

edit
close

play_arrow

link
brightness_4
code

// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
  
// Function to return the nth term
// of the given series
int oddTriangularNumber(int N)
{
    return (N * ((2 * N) - 1));
}
  
// Driver code
int main()
{
    int N = 3;
    cout << oddTriangularNumber(N);
  
    return 0;
}

chevron_right


Java

filter_none

edit
close

play_arrow

link
brightness_4
code

// Java implementation of the approach
class GFG
{
  
// Function to return the nth term
// of the given series
static int oddTriangularNumber(int N)
{
    return (N * ((2 * N) - 1));
}
  
// Driver code
public static void main(String[] args) 
{
    int N = 3;
    System.out.println(oddTriangularNumber(N));
}
}
  
// This code contributed by Rajput-Ji

chevron_right


Python3

filter_none

edit
close

play_arrow

link
brightness_4
code

# Python 3 implementation of the approach
  
# Function to return the nth term
# of the given series
def oddTriangularNumber(N):
    return (N * ((2 * N) - 1))
  
# Driver code
if __name__ == '__main__':
    N = 3
    print(oddTriangularNumber(N))
  
# This code is contributed by
# Surendra_Gangwar

chevron_right


C#

filter_none

edit
close

play_arrow

link
brightness_4
code

// C# implementation of the approach 
using System;
  
class GFG 
  
    // Function to return the nth term 
    // of the given series 
    static int oddTriangularNumber(int N) 
    
        return (N * ((2 * N) - 1)); 
    
      
    // Driver code 
    public static void Main(String[] args) 
    
        int N = 3; 
        Console.WriteLine(oddTriangularNumber(N)); 
    
  
/* This code contributed by PrinciRaj1992 */

chevron_right


PHP

filter_none

edit
close

play_arrow

link
brightness_4
code

<?php
// PHP implementation of the approach 
  
// Function to return the nth term 
// of the given series 
function oddTriangularNumber($N
    return ($N * ((2 * $N) - 1)); 
  
    // Driver code 
    $N = 3; 
    echo oddTriangularNumber($N); 
      
    // This code is contributed by Ryuga
  
?>

chevron_right


Output:

15


My Personal Notes arrow_drop_up

Check out this Author's contributed articles.

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.