# n’th Pentagonal Number

Given an integer n, find the nth Pentagonal number. First three pentagonal numbers are 1, 5 and 12 (Please see below diagram).

The n’th pentagonal number P_{n} is the number of distinct dots in a pattern of dots consisting of the outlines of regular pentagons with sides up to n dots, when the pentagons are overlaid so that they share one vertex [Source Wiki]

**Examples :**

Input:n = 1Output:1Input:n = 2Output:5Input:n = 3Output:12

In general, a polygonal number (triangular number, square number, etc) is a number represented as dots or pebbles arranged in the shape of a regular polygon. The first few pentagonal numbers are: 1, 5, 12, etc.

If s is the number of sides in a polygon, the formula for the nth s-gonal number P (s, n) is

nth s-gonal number P(s, n) = (s - 2)n(n-1)/2 + n If we put s = 5, we get n'th Pentagonal number P_{n}= 3*n*(n-1)/2 + n

Examples:

**Pentagonal Number**

Below are the implementations of above idea in different programming languages.

## C/C++

`// C program for above approach ` `#include <stdio.h> ` `#include <stdlib.h> ` ` ` `// Finding the nth Pentagonal Number ` `int` `pentagonalNum(` `int` `n) ` `{ ` ` ` `return` `(3*n*n - n)/2; ` `} ` ` ` `// Driver program to test above function ` `int` `main() ` `{ ` ` ` `int` `n = 10; ` ` ` `printf` `(` `"10th Pentagonal Number is = %d \n \n"` `, ` ` ` `pentagonalNum(n)); ` ` ` ` ` `return` `0; ` `} ` |

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## Java

`// Java program for above approach ` `class` `Pentagonal ` `{ ` ` ` `int` `pentagonalNum(` `int` `n) ` ` ` `{ ` ` ` `return` `(` `3` `*n*n - n)/` `2` `; ` ` ` `} ` `} ` ` ` `public` `class` `GeeksCode ` `{ ` ` ` `public` `static` `void` `main(String[] args) ` ` ` `{ ` ` ` `Pentagonal obj = ` `new` `Pentagonal(); ` ` ` `int` `n = ` `10` `; ` ` ` `System.out.printf(` `"10th petagonal number is = "` ` ` `+ obj.pentagonalNum(n)); ` ` ` `} ` `} ` |

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## Python

`# Python program for finding pentagonal numbers ` `def` `pentagonalNum( n ): ` ` ` `return` `(` `3` `*` `n` `*` `n ` `-` `n)` `/` `2` `#Script Begins ` ` ` `n ` `=` `10` `print` `"10th Pentagonal Number is = "` `, pentagonalNum(n) ` ` ` `#Scripts Ends ` |

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## C#

`// C# program for above approach ` `using` `System; ` ` ` `class` `GFG { ` ` ` ` ` `static` `int` `pentagonalNum(` `int` `n) ` ` ` `{ ` ` ` `return` `(3 * n * n - n) / 2; ` ` ` `} ` ` ` ` ` `public` `static` `void` `Main() ` ` ` `{ ` ` ` `int` `n = 10; ` ` ` ` ` `Console.WriteLine(` `"10th petagonal"` ` ` `+ ` `" number is = "` `+ pentagonalNum(n)); ` ` ` `} ` `} ` ` ` `// This code is contributed by vt_m. ` |

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## PHP

`<?php ` `// PHP program for above approach ` ` ` `// Finding the nth Pentagonal Number ` `function` `pentagonalNum(` `$n` `) ` `{ ` ` ` `return` `(3 * ` `$n` `* ` `$n` `- ` `$n` `) / 2; ` `} ` ` ` `// Driver Code ` `$n` `= 10; ` `echo` `"10th Pentagonal Number is = "` `, ` ` ` `pentagonalNum(` `$n` `); ` ` ` `// This code is contributed by ajit ` `?> ` |

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**Output :**

10th Pentagonal Number is = 145

Reference:

https://en.wikipedia.org/wiki/Polygonal_number

This article is contributed by **Mazhar Imam Khan**. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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