# Program to check if N is a Pentagonal Number in C++

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Given with a number N the task is to check whether the number is a pentagonal number or not. Numbers that can be arranged to form a pentagon is a pentagonal number as these numbers can be used as points to form a pentagon. For example, some of pentagonal numbers are 1, 5, 12, 22, 35, 51....

We can use formula to check whether the number is a pentagonal number or not

$$p(n)=\frac{\text{3}*n^2-n}{\text{2}}$$

Where, n is the number of points pentagonal will have

## Example

Input-: n=22
Output-: 22 is pentagonal number
Input-: n=23
Output-: 23 is not a pentagonal number

## Algorithm

Start
Step 1 -> declare function to Check N is pentagonal or not
bool check(int n)
declare variables as int i = 1, a
do
set a = (3*i*i - i)/2
set i += 1
while ( a < n );
return (a == n);
Step 2 -> In main()
Declare int n = 22
If (check(n))
Print is pentagonal
End
Else
Print it is not pentagonal
End
Stop

## Example

#include <iostream>
using namespace std;
// check N is pentagonal or not.
bool check(int n){
int i = 1, a;
do{
a = (3*i*i - i)/2;
i += 1;
}
while ( a < n );
return (a == n);
}
int main(){
int n = 22;
if (check(n))
cout << n << " is pentagonal " << endl;
else
cout << n << " is not pentagonal" << endl;
return 0;
}

## Output

22 is pentagonal
Updated on 23-Sep-2019 11:37:11