Program to find the Nth term of the series 0, 5, 14, 27, 44, ……..

Given a number N. The task is to write a program to find the Nth term in the below series:

0, 5, 14, 27, 44 …(Nth Term)

Examples:



Input: N = 4
Output: 27
For N = 4,
Nth term = ( 2 * N * N - N - 1 ) 
         = ( 2 * 4 * 4 - 4 - 1 ) 
         = 27

Input: N = 10
Output: 188

Approach: The generalized Nth term of this series:

Nth Term: 2 * N * N - N - 1 

Below is the required implementation:

C++

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// CPP program to find N-th term of the series:
// 0, 5, 14, 27, 44 ...
#include <iostream>
#include <math.h>
using namespace std;
  
// Calculate Nth term of series
int nthTerm(int n)
{
    return 2 * pow(n, 2) - n - 1;
}
  
// Driver code
int main()
{
    int N = 4;
  
    cout << nthTerm(N);
  
    return 0;
}

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Java

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// Java program to find N-th term of the series:
// 0, 5, 14, 27, 44 ...
import java.util.*;
  
class solution
{
  
// Calculate Nth term of series
static int nthTerm(int n)
{
    return 2 *(int)Math.pow(n, 2) - n - 1;
}
  
// Driver code
public static void main(String arr[])
{
    int N = 4;
  
    System.out.println(nthTerm(N));
}
}
//This code is contributed by Surendra_Gangwar

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Python 3

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# Python 3 program to find 
# N-th term of the series:
# 0, 5, 14, 27, 44 ...
  
# Calculate Nth term of series
def nthTerm(n):
  
    return 2 * pow(n, 2) - n - 1
  
# Driver code
if __name__ == "__main__":
    N = 4
  
    print(nthTerm(N))
  
# This code is contributed 
# by ChitraNayal

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C#

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// C# program to find 
// N-th term of the series: 
// 0, 5, 14, 27, 44 ... 
using System;
class GFG 
  
// Calculate Nth term of series 
static int nthTerm(int n) 
    return 2 * (int)Math.Pow(n, 2) - n - 1; 
  
// Driver code 
static public void Main ()
    int N = 4; 
      
    Console.Write(nthTerm(N)); 
  
// This code is contributed by Raj

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PHP

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<?php
// PHP program to find 
// N-th term of the series:
// 0, 5, 14, 27, 44 ...
  
// Calculate Nth term of series
function nthTerm($n)
{
    return 2 * pow($n, 2) - $n - 1;
}
  
// Driver code
$N = 4;
  
echo nthTerm($N);
  
// This code is contributed 
// by Akanksha Rai(Abby_akku)
?>

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Output:

27

Time Complexity: O(1)

Note: Sum upto n terms of the above series(Sn) is:

$  S_n = 2 \sum_{i=1}^n n^2 - \sum_{i=1}^n n  -1\\ S_n=\frac{2n(n+1)(2n+1)}{6}-\frac{n(n+1)}{2}-n\\ S_n=\frac{n(n+1)(4n-1)-24}{6}\\ $



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