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# n’th Pentagonal Number

• Difficulty Level : Medium
• Last Updated : 16 Jul, 2021

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 Pn 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 = 1
Output: 1

Input: n = 2
Output: 5

Input: n = 3
Output: 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 Pn = 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#includeusing namespace std; // Finding the nth pentagonal numberint pentagonalNum(int n){    return (3 * n * n - n) / 2;} // Driver codeint 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 #include  // Finding the nth Pentagonal Numberint pentagonalNum(int n){    return (3*n*n - n)/2;} // Driver program to test above functionint main(){    int n = 10;    printf("10th Pentagonal Number is = %d \n \n",                             pentagonalNum(n));     return 0;}

## Java

 // Java program for above approachclass 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 numbersdef pentagonalNum( n ):    return (3*n*n - n)/2#Script Begins n = 10print "10th Pentagonal Number is = ", pentagonalNum(n)  #Scripts Ends

## C#

 // C# program for above approachusing 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.



## Javascript



Output :

10th Pentagonal Number is = 145

Time Complexity: O(1)
Auxiliary Space: O(1)
Reference:
https://en.wikipedia.org/wiki/Polygonal_number
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