Find nth term of the series 5 2 13 41

Given a number N, the task is to find the nth term of the series

5, 2, 19, 13, 41, 31, 71, 57….

It is given that value of n can range between 1 and 10000.



Examples:

Input: N = 4
Output:13

Input: N = 15
Output:272

Approach: The problem looks very hard but approach is very simple. If the value of n is given as an odd number, the nth term will be ( ( n + 1 ) ^ 2 ) + n.
Otherwise, it will be ( ( n – 1 ) ^ 2 ) + n.

Implementation:

C++

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// C++ program to find nth term of 
// the series 5 2 13 41
#include<bits/stdc++.h>
using namespace std;
  
// function to calculate nth term of the series
int nthTermOfTheSeries(int n)
{
    // to store the nth term of series
    int nthTerm;
  
    // if n is even number
    if (n % 2 == 0)
        nthTerm = pow(n - 1, 2) + n;
  
    // if n is odd number
    else
        nthTerm = pow(n + 1, 2) + n;
  
    // return nth term
    return nthTerm;
}
  
// Driver code
int main()
{
    int n;
  
    n = 8;
    cout << nthTermOfTheSeries(n) << endl;
  
    n = 12;
    cout << nthTermOfTheSeries(n) << endl;
  
    n = 102;
    cout << nthTermOfTheSeries(n) << endl;
  
    n = 999;
    cout << nthTermOfTheSeries(n) << endl;
  
    n = 9999;
    cout << nthTermOfTheSeries(n) << endl;
  
    return 0;
}
  
// This code is contributed
// by Akanksha Rai

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C

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// C program to find nth term of 
// the series 5 2 13 41
#include <math.h>
#include <stdio.h>
  
// function to calculate nth term of the series
int nthTermOfTheSeries(int n)
{
    // to store the nth term of series
    int nthTerm;
  
    // if n is even number
    if (n % 2 == 0)
        nthTerm = pow(n - 1, 2) + n;
  
    // if n is odd number
    else
        nthTerm = pow(n + 1, 2) + n;
  
    // return nth term
    return nthTerm;
}
  
// Driver code
int main()
{
    int n;
  
    n = 8;
  
    printf("%d\n", nthTermOfTheSeries(n));
  
    n = 12;
    printf("%d\n", nthTermOfTheSeries(n));
  
    n = 102;
    printf("%d\n", nthTermOfTheSeries(n));
  
    n = 999;
    printf("%d\n", nthTermOfTheSeries(n));
  
    n = 9999;
    printf("%d\n", nthTermOfTheSeries(n));
  
    return 0;
}

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Java

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// Java program to find nth term of the series 5 2 13 41
  
import java.lang.Math;
class GFG
{
// function to calculate nth term of the series
static long  nthTermOfTheSeries(int n)
{
    // to store the nth term of series
    long nthTerm;
  
    // if n is even number
    if (n % 2 == 0)
        nthTerm = (long)Math.pow(n - 1, 2) + n;
  
    // if n is odd number
    else
        nthTerm = (long)Math.pow(n + 1, 2) + n;
  
    // return nth term
    return nthTerm;
}
  
// Driver code
public static void main(String[] args)
{
    int n;
  
    n = 8;
  
    System.out.println( nthTermOfTheSeries(n));
  
    n = 12;
    System.out.println( nthTermOfTheSeries(n));
  
    n = 102;
    System.out.println( nthTermOfTheSeries(n));
  
    n = 999;
    System.out.println( nthTermOfTheSeries(n));
      
    n = 9999;
    System.out.println( nthTermOfTheSeries(n));
//This code is contributed by  29AjayKumar
  
}
}

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Python3

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# Python3 program to find nth term 
# of the series 5 2 13 41
from math import pow
  
# function to calculate nth term 
# of the series
def nthTermOfTheSeries(n):
      
    # to store the nth term of series
    # if n is even number
    if (n % 2 == 0):
        nthTerm = pow(n - 1, 2) + n
  
    # if n is odd number
    else:
        nthTerm = pow(n + 1, 2) + n
  
    # return nth term
    return nthTerm
  
# Driver code
if __name__ == '__main__':
      
    n = 8
    print(int(nthTermOfTheSeries(n)))
  
    n = 12
    print(int(nthTermOfTheSeries(n)))
  
    n = 102
    print(int(nthTermOfTheSeries(n)))
  
    n = 999
    print(int(nthTermOfTheSeries(n)))
  
    n = 9999
    print(int(nthTermOfTheSeries(n)))
  
# This code is contributed by
# Shashank_Sharma

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C#

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// C# program to find nth term 
// of the series 5 2 13 41 
using System;
  
class GFG 
    // function to calculate 
    // nth term of the series 
    static long nthTermOfTheSeries(int n) 
    
        // to store the nth term of series 
        long nthTerm; 
      
        // if n is even number 
        if (n % 2 == 0) 
            nthTerm = (long)Math.Pow(n - 1, 2) + n; 
      
        // if n is odd number 
        else
            nthTerm = (long)Math.Pow(n + 1, 2) + n; 
      
        // return nth term 
        return nthTerm; 
    
      
    // Driver code 
    public static void Main() 
    
        int n; 
      
        n = 8; 
        Console.WriteLine(nthTermOfTheSeries(n)); 
      
        n = 12; 
        Console.WriteLine( nthTermOfTheSeries(n)); 
      
        n = 102; 
        Console.WriteLine( nthTermOfTheSeries(n)); 
      
        n = 999; 
        Console.WriteLine( nthTermOfTheSeries(n)); 
          
        n = 9999; 
        Console.WriteLine( nthTermOfTheSeries(n)); 
    }
  
// This code is contributed by Ryuga 

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PHP

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<?php 
// Php program to find nth term of 
// the series 5 2 13 41
  
// function to calculate nth term 
// of the series
function nthTermOfTheSeries($n)
{
  
    // if n is even number
    if ($n % 2 == 0)
        $nthTerm = pow($n - 1, 2) + $n;
  
    // if n is odd number
    else
        $nthTerm = pow($n + 1, 2) + $n;
  
    // return nth term
    return $nthTerm;
}
  
// Driver code
$n = 8;
echo nthTermOfTheSeries($n) . "\n";
  
$n = 12;
echo nthTermOfTheSeries($n) . "\n";
  
$n = 102;
echo nthTermOfTheSeries($n) . "\n";
  
$n = 999;
echo nthTermOfTheSeries($n) . "\n";
  
$n = 9999;
echo nthTermOfTheSeries($n) . "\n";
  
// This code is contributed by ita_c
?>

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Output:

57
133
10303
1000999
100009999


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