Program to find Nth term in the given Series

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

1, 1, 2, 3, 4, 9, 8, 27, 16, 81, 32, 243, 64, 729, 128, 2187…

Examples:

Input : 4
Output : 3

Input :  11
Output : 32

On observing carefully, you will find that the series is a mixture of 2 series:

  1. All the odd terms in this series form a geometric series.
  2. All the even terms form yet another geometric series.

The approach to solving the problem is quite simple. The odd positioned terms in the given series form a GP series with first term = 1 and common ration = 2. Similarly, the even positioned terms in the given series form a GP series with first term = 1 and common ration = 3.



Therefore first check whether the input number N is even or odd. If it is even, set N=N/2(since there are Two GP series running parallely) and find the Nth term by using formula an = a1·rn-1 with r=3.

Similarly, if N is odd, set N=(n/2)+1 and do the same as previous with r=2.

Below is the implementation of above approach:

filter_none

edit
close

play_arrow

link
brightness_4
code

// C++ program to find Nth term 
// in the given Series
#include <iostream>
#include <math.h>
  
using namespace std;
  
// Function to find the nth term 
// in the given series
void findNthTerm(int n)
{
    // If input number is even
    if (n % 2 == 0) {
        n = n / 2;
        cout << pow(3, n - 1) << endl;
    }
    // If input number is odd
    else {
        n = (n / 2) + 1;
        cout << pow(2, n - 1) << endl;
    }
}
  
// Driver Code
int main()
{
    int N = 4;
    findNthTerm(N);
  
    N = 11;
    findNthTerm(N);
  
    return 0;
}
chevron_right

filter_none

edit
close

play_arrow

link
brightness_4
code

// Java program to find Nth term 
// in the given Series
import java.io.*;
import java.util.*;
import java.lang.*;
  
class GFG
{
// Function to find the nth term 
// in the given series
static void findNthTerm(int n)
{
    // If input number is even
    if (n % 2 == 0)
    {
        n = n / 2;
        System.out.print(Math.pow(3, n - 1) + "\n");
    }
    // If input number is odd
    else 
    {
        n = (n / 2) + 1;
        System.out.print(Math.pow(2, n - 1) + "\n");
    }
}
  
// Driver Code
public static void main(String[] args)
{
    int N = 4;
    findNthTerm(N);
  
    N = 11;
    findNthTerm(N);
  
}
}
  
// This code is contributed 
// by Akanksha Rai(Abby_akku)
chevron_right

filter_none

edit
close

play_arrow

link
brightness_4
code

# Python3 program to find Nth term 
# in the given Series
  
# Function to find the nth term 
# in the given series
def findNthTerm(n):
    # If input number is even
    if n % 2 == 0:
        n //= 2
        print(3 ** (n - 1))
    # If input number is odd
    else:
        n = (n // 2) + 1
        print(2 ** (n - 1))
  
# Driver Code
if __name__=='__main__':
    N = 4
    findNthTerm(N)
  
    N = 11
    findNthTerm(N)
  
# This code is contributed
# by vaibhav29498
chevron_right

filter_none

edit
close

play_arrow

link
brightness_4
code

// C# program to find Nth term 
// in the given Series
using System;
  
class GFG
{
// Function to find the nth
// term in the given series
static void findNthTerm(int n)
{
    // If input number is even
    if (n % 2 == 0)
    {
        n = n / 2;
        Console.WriteLine(Math.Pow(3, n - 1));
    }
      
    // If input number is odd
    else
    {
        n = (n / 2) + 1;
        Console.WriteLine(Math.Pow(2, n - 1));
    }
}
  
// Driver Code
public static void Main()
{
    int N = 4;
    findNthTerm(N);
  
    N = 11;
    findNthTerm(N);
}
}
  
// This code is contributed 
// by chandan_jnu.
chevron_right

filter_none

edit
close

play_arrow

link
brightness_4
code

<?php
// php program to find Nth term 
// in the given Series
  
// Function to find the nth term 
// in the given series
function findNthTerm($n)
{
    // If input number is even
    if ($n % 2 == 0) 
    {
        $n = $n / 2;
        echo pow(3, $n - 1) . "\n";
    }
    // If input number is odd
    else
    {
        $n = ($n / 2) + 1;
        echo pow(2, intval($n - 1)) . "\n";
    }
}
  
// Driver Code
$N = 4;
findNthTerm($N);
  
$N = 11;
findNthTerm($N);
  
// This code is contributed 
// by Akanksha Rai(Abby_akku)
?>
chevron_right

Output:
3
32




Check out this Author's contributed articles.

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.



Article Tags :
Practice Tags :