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Find the 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.
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