# Program to find Nth term in the given Series

• Difficulty Level : Medium
• Last Updated : 28 May, 2022

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 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

 ``

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.

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