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

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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++

// 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; 
} 

Java

// 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)); 
    }     
} 

Python 3

# 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 

C#

// 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 

PHP

<?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 
?> 

Javascript

<script> 
  
// JavaScript 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 Function 
  
    let N = 3; 
    document.write(nthTerm(N)); 
      
// This code contributed by Rajput-Ji  
  
</script> 

Output:

Time Complexity: O(1)

Space Complexity: O(1) because constant variables are used

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