# n’th Pentagonal Number

Given an integer n, find the nth Pentagonal number. The 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 the above idea in different programming languages.

## C++

`// C++ program for above approach` `#include<bits/stdc++.h>` `using` `namespace` `std;` `// Finding the nth pentagonal number` `int` `pentagonalNum(` `int` `n)` `{` ` ` `return` `(3 * n * n - n) / 2;` `}` `// Driver code` `int` `main()` `{` ` ` `int` `n = 10;` ` ` ` ` `cout << ` `"10th Pentagonal Number is = "` ` ` `<< pentagonalNum(n);` ` ` `return` `0;` `}` `// This code is contributed by Code_Mech` |

## 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;` `}` |

## 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));` ` ` `}` `}` |

## 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` |

## 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.` |

## 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` `?>` |

## Javascript

`<script>` `// Javascript program for above approach` ` ` `function` `pentagonalNum(n)` ` ` `{` ` ` `return` `(3 * n * n - n) / 2;` ` ` `}` `// Driver code to test above methods` ` ` `let n = 10;` ` ` ` ` `document.write(` `"10th petagonal"` ` ` `+ ` `" number is = "` `+ pentagonalNum(n));` ` ` ` ` `// This code is contributed by avijitmondal1998.` `</script>` |

**Output :**

10th Pentagonal Number is = 145

**Time Complexity:** O(1)**Auxiliary Space:** O(1)

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 write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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