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:

- All the odd terms in this series form a geometric series.
- 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 **a _{n} = a_{1}·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; ` `} ` |

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## 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) ` |

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## 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 ` |

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## 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. ` |

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## 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) ` `?> ` |

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**Output:**

3 32

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