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Program to find the Nth term of the series 3, 7, 13, 21, 31…..

Given a number N, the task is to find the Nth term of this series:

3, 7, 13, 21, 31, …….

Examples: 

Input: N = 4
Output: 21
Explanation:
Nth term = (pow(N, 2) + N + 1)
= (pow(4, 2) + 4 + 1)
= 21
Input: N = 11
Output: 133

Approach:

Subtracting these two equations we get 

Therefore, the Nth Term of the given series is: 

Below is the implementation of the above approach: 

// CPP program to find the Nth term of given series.
#include <iostream>
#include <math.h>
using namespace std;
 
// Function to calculate sum
long long int getNthTerm(long long int N)
{
    // Return Nth term
    return (pow(N, 2) + N + 1);
}
 
// driver code
int main()
{
    // declaration of number of terms
    long long int N = 11;
 
    // Get the Nth term
    cout << getNthTerm(N);
 
    return 0;
}

                    
// Java code to find the Nth term of given series.
import java.util.*;
 
class solution
{
 
// Function to calculate sum
static long getNthTerm(long N)
{
     
   // Return Nth term
    return ((int)Math.pow(N, 2) + N + 1);
}
 
//Driver program
public static void main(String arr[])
{
     
   // declaration of number of terms
    long N = 11;
 
    // Get the Nth term
    System.out.println(getNthTerm(N));
 
}
}
//THis code is contributed by
//Surendra_Gangwar

                    
# Python3 Code to find the
# Nth term of given series.
 
# Function to calculate sum
def getNthTerm(N):
     
    # Return Nth term
    return (pow(N, 2) + N + 1)
 
# driver code
if __name__=='__main__':
     
# declaration of number of terms
    N = 11
     
# Get the Nth term
    print(getNthTerm(N))
 
# This code is contributed by
# Sanjit_Prasad

                    
// C# code to find the Nth
// term of given series.
using System;
 
class GFG
{
 
// Function to calculate sum
static long getNthTerm(long N)
{
     
// Return Nth term
    return ((int)Math.Pow(N, 2) + N + 1);
}
 
// Driver Code
static public void Main ()
{
     
    // declaration of number
    // of terms
    long N = 11;
 
    // Get the Nth term
    Console.Write(getNthTerm(N));
}
}
 
// This code is contributed by Raj

                    
<script>
// JavaScript program to find the Nth term of given series.
 
// Function to calculate sum
function getNthTerm(N)
{
    // Return Nth term
    return (Math.pow(N, 2) + N + 1);
}
   
// driver code
 
   // declaration of number of terms
   let N = 11;
   
   // Get the Nth term
   document.write(getNthTerm(N));
   
// This code is contributed by Surbhi Tyagi
 
</script>

                    
<?php
// PHP program to find the
// Nth term of given series
 
// Function to calculate sum
function getNthTerm($N)
{
    // Return Nth term
    return (pow($N, 2) + $N + 1);
}
 
// Driver code
 
// declaration of number of terms
$N = 11;
 
// Get the Nth term
echo getNthTerm($N);
 
// This code is contributed by Raj
?>

                    

Output
133



Time Complexity: O(1)
Space Complexity: O(1) since using constant variables
 

Method 2: We can also solve the problem by the formula [ (n+1)2-n  ]. 

// CPP program to find the Nth term of given series.
#include <iostream>
#include <math.h>
using namespace std;
 
// Function to calculate sum
long long int getNthTerm(long long int N)
{
    // Return Nth term
    return (pow(N + 1, 2) - N);
}
 
// driver code
int main()
{
    // declaration of number of terms
    long long int N = 11;
 
    // Get the Nth term
    cout << getNthTerm(N);
 
    return 0;
}

                    
// Nikunj Sonigara
 
public class Main {
 
    static long getNthTerm(long N) {
        return (long) (Math.pow(N + 1, 2) - N);
    }
 
    public static void main(String[] args) {
        long N = 11;
        System.out.println(getNthTerm(N));
    }
}

                    
# Python program to find the Nth term of given series.
import math
 
# Function to calculate sum
def getNthTerm(N):
    # Return Nth term
    return int(math.pow(N + 1, 2) - N)
 
# driver code
if __name__ == '__main__':
    # declaration of number of terms
    N = 11
 
    # Get the Nth term
    print(getNthTerm(N))

                    
using System;
 
class Program {
    // Function to calculate the Nth term of the series
    static long GetNthTerm(long N)
    {
        // Return Nth term
        return (long)(Math.Pow(N + 1, 2) - N);
    }
 
    static void Main()
    {
        // Declaration of the number of terms
        long N = 11;
 
        // Get the Nth term
        Console.WriteLine(GetNthTerm(N));
    }
}

                    
// Nikunj Sonigara
 
function getNthTerm(N) {
    return Math.pow(N + 1, 2) - N;
}
 
const N = 11;
console.log(getNthTerm(N));

                    

Output
133



Time Complexity: O(logN)
Space Complexity: O(1) since using constant variables


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