Find Pentagonal Pyramidal Number Using C++

A pentagonal pyramidal number is equal to the number of items in a pentagonal base pyramid. Look at some Pentagonal numbers below.

Sum of Pentagonal Numbers till N equals to Nth Pentagonal Pyramidal Number. In this article, we will discuss finding the Nth Pentagonal Pyramidal number, for example

Input : N = 4
Output : 40
Explanation : Sum of first four pentagonal numbers 1, 5, 12, 22 is 40.

Input : N = 6
Output : 126
Explanation : Sum of first four pentagonal numbers 1, 5, 12, 22, 35, 51 is 40.

Approach to find The Solution

Simple Approach

As per the example, the simplest approach comes to mind: traverse the number from 1 to N and keep adding the pentagonal numbers. The pentagonal number can be found by the formula (3 * n2 - n) / 2

e.g For n = 2, pentagonal number = (3 * 22 - 2)/2 = 5

Example

#include <bits/stdc++.h>
using namespace std;

int main () {
   int N = 6, SUM = 0;

   // traversing from number 1 to N.
   for (int i = 1; i <= N; i++) {
      // Calculating ith pentagonal number
      // and adding to the SUM.
      SUM = SUM + (3 * i * i - i) / 2;
   }
   cout <<"Nth Pentagonal Pyramidal Number: "<< SUM << endl;
   return 0;
}

Output

Nth Pentagonal Pyramidal Number: 126

Efficient Approach

The program can be efficient by using a formula to find N Pentagonal Pyramidal Number, which is n2 * (n + 1) / 2.

Example

#include <bits/stdc++.h>
using namespace std;

int main() {
   int N = 6, result;
   // calculating Nth pentagonal pyramidal number by formula.
   result = N * N * (N + 1) / 2;
   cout <<"Nth Pentagonal Pyramidal Number: " << result << endl;
   return 0;
}

Output

Nth Pentagonal Pyramidal Number: 126

Conclusion

In this article, we discussed the problem of finding the Nth Pentagonal Pyramidal Number. We discussed two approaches to solving this problem: traversing till Nth number and using a formula. We also discussed the C++ program to solve for the same. We can write the same code in other programming languages like C, Java, Python, etc. We hope you find this article helpful.