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:

**Triangular number**

**Square number**

**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; }

## 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

Output:

10th Pentagonal Number is = 145

Reference:

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

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