Find Nth term of the series 5, 13, 25, 41, 61…

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

5, 13, 25, 41, 61...

Examples:

Input : 3
Output : 25
For N = 3
Nth term = 3*3 + (3+1)*(3+1)
         = 25
Input : 5
Output : 61

On observing carefully, the Nth term of the given series can be generalised as:

Nth term = N2 + (N+1)2

Below is the implementation of the above approach:

C++

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// CPP program to find N-th term of the series:
// 5, 13, 25, 41, 61...
#include <iostream>
using namespace std;
  
// calculate Nth term of series
int nthTerm(int N)
{
    return N * N + (N + 1) * (N + 1);
}
  
// Driver Function
int main()
{
    int N = 3;
  
    cout << nthTerm(N);
  
    return 0;
}

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Java

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// Java program to calculate Nth term of 
// the series: 5, 13, 25, 41, 61...
  
import java.io.*;
  
class Nth {
    public static int nthTerm(int N)
    {
        // By using above formula
        return N * N + (N + 1) * (N + 1);
    }
      
    public static void main(String[] args)
    {
        int N = 3; // Nth term is 25
          
        // call and print Nth term
        System.out.println(nthTerm(N));
    }    
}

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Python 3

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# Python 3 program to find 
# N-th term of the series:
# 5, 13, 25, 41, 61... 
  
# Function to calculate
# Nth term of series
def nthTerm(N) :
    return N * N + (N + 1) * (N + 1)
  
# Driver Code
if __name__ == "__main__" :
  
    N = 3
  
    # function calling
    print(nthTerm(N))
  
# This code is contributed 
# by ANKITRAI1

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C#

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// C# program to calculate Nth term of 
// the series: 5, 13, 25, 41, 61...
using System;
  
class GFG 
{
public static int nthTerm(int N)
{
    // By using above formula
    return N * N + (N + 1) * (N + 1);
}
  
// Driver Code
public static void Main()
{
    int N = 3; // Nth term is 25
      
    // call and print Nth term
    Console.Write(nthTerm(N));
}
  
// This code is contributed 
// by ChitraNayal

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PHP

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<?php 
// PHP program to find N-th
// term of the series:
// 5, 13, 25, 41, 61...
  
// calculate Nth term of series
function nthTerm($N)
{
    return $N * $N + ($N + 1) * 
                     ($N + 1);
}
  
// Driver Code
$N = 3;
  
echo nthTerm($N);
  
// This code is contributed 
// by ChitraNayal
?>

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Output:

25

Time Complexity: O(1)



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Improved By : AnkitRai01, Ita_c