# 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
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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:

 `// 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 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 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# 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. `

 ` `

Output:
```3
32
```

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