# Program to find Nth term in the given Series

• Difficulty Level : Hard
• Last Updated : 01 Nov, 2021

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…

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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 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:

## C++

 `// C++ program to find Nth term``// in the given Series``#include ``#include ` `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

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## Javascript

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Output:
```3
32```

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