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 parallelly) and find the Nth term by using formula a_n = a₁·r^n-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: 

C++

// 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;
}

Java

// 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)

Python3

# 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

C#

// 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.

PHP

<?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)
?>

Javascript

<script>

// JavaScript 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 = Math.floor(n / 2);
            document.write(Math.pow(3, n - 1) + "<br>");
        }
        // If input number is odd
        else {
            n = Math.floor(n / 2) + 1;
            document.write(Math.pow(2, n - 1) + "<br>");
        }
    }

    // Driver Code

    let N = 4;
    findNthTerm(N);

    N = 11;
    findNthTerm(N);

// This code is contributed by Mayank Tyagi

</script>

Output:

3
32

Time Complexity: O(log₂n), where n represents the given integer.
Auxiliary Space: O(1), no extra space is required, so it is a constant.