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:

 Sum = 0+3+7+13+21+31+........+a_{n-1} + a_n\\  Sum = 3+7+13+21+31+...+a_{n-2}+a_{n-1}+a_n
Subtracting these two equations we get
$ 0=3+\left \{\frac{n-1}{2}\right \}[2*4 + (n-2)*2]-a_n\\  =3+\left \{\frac{n-1}{2}\right \}[8 + 2n-4]-a_n\\  =3+\left \{\frac{n-1}{2}\right \}[2n+4]-a_n\\  a_n=3+(n-1)(n+2)\\  a_n=n^2+n+1  $

Therefore, the Nth Term of the given series is:

a_n=n^2+n+1

Below is the implementation of the above approach:

C++

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// 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;
}

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Java

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// 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 contibuted by
//Surendra_Gangwar

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Python3

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# 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

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C#

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// 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 contibuted by Raj

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PHP

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<?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
?>

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Output:

133

Time Complexity: O(1)



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