Find the sum of the first Nth Centered Pentadecagonal Number
Given a number N the task is to find the sum of the first N Centered Pentadecagonal Number.
The first few Centered Pentadecagonal Numbers are 1, 16, 46, 91, 151, 226, 316 …
Examples:
Input: N = 3
Output: 63
Explanation:
1, 16 and 46 are the first three centered pentadecagonal numbers.Input: N = 5
Output: 305
Approach:
- Initially, we need to create a function which will help us to calculate the Nth centered Pentadecagonal number.
- Now, run a loop starting from 1 to N, to find ith Centered Pentadecagonal number.
- Add all the above calculated Centered Pentadecagonal numbers.
- Finally, display the sum of 1st N Centered Pentadecagonal numbers.
Below is the implementation of the above approach:
C++
// C++ program to find the sum of the // first N centered pentadecagonal number #include<bits/stdc++.h> using namespace std; // Function to find the centered // pentadecagonal number int Centered_Pentadecagonal_num( int n) { // Formula to calculate // N-th centered pentadecagonal // number return (15 * n * n - 15 * n + 2) / 2; } // Function to find the sum of // the first N centered // pentadecagonal numbers int sum_Centered_Pentadecagonal_num( int n) { // Variable to store // the sum int summ = 0; for ( int i = 1; i < n + 1; i++) { summ += Centered_Pentadecagonal_num(i); } return summ; } // Driver Code int main() { int n = 5; cout << sum_Centered_Pentadecagonal_num(n); return 0; } // This code is contributed by Rajput-Ji |
Java
// Java program to find the sum of the // first N centered pentadecagonal number class GFG { // Function to find the centered // pentadecagonal number static int Centered_Pentadecagonal_num( int n) { // Formula to calculate // N-th centered pentadecagonal // number return ( 15 * n * n - 15 * n + 2 ) / 2 ; } // Function to find the sum of // the first N centered // pentadecagonal numbers static int sum_Centered_Pentadecagonal_num( int n) { // Variable to store // the sum int summ = 0 ; for ( int i = 1 ; i < n + 1 ; i++) { summ += Centered_Pentadecagonal_num(i); } return summ; } // Driver Code public static void main(String[] args) { int n = 5 ; System.out.println(sum_Centered_Pentadecagonal_num(n)); } } // This code is contributed by sapnasingh4991 |
Python3
# Python3 program to find the sum # of the first N centered # Pentadecagonal number # Function to find the # Centered_Pentadecagonal # number def Centered_Pentadecagonal_num(n): # Formula to calculate # N-th Centered_Pentadecagonal # number return ( 15 * n * n - 15 * n + 2 ) / / 2 # Function to find the # sum of the first N # Centered_Pentadecagonal # numbers def sum_Centered_Pentadecagonal_num(n) : # Variable to store # the sum summ = 0 for i in range ( 1 , n + 1 ): summ + = Centered_Pentadecagonal_num(i) return summ # Driver code if __name__ = = '__main__' : n = 5 print (sum_Centered_Pentadecagonal_num(n)) |
C#
// C# program to find the sum of the // first N centered pentadecagonal number using System; class GFG { // Function to find the centered // pentadecagonal number static int Centered_Pentadecagonal_num( int n) { // Formula to calculate // N-th centered pentadecagonal // number return (15 * n * n - 15 * n + 2) / 2; } // Function to find the sum of // the first N centered // pentadecagonal numbers static int sum_Centered_Pentadecagonal_num( int n) { // Variable to store // the sum int summ = 0; for ( int i = 1; i < n + 1; i++) { summ += Centered_Pentadecagonal_num(i); } return summ; } // Driver Code public static void Main(String[] args) { int n = 5; Console.WriteLine(sum_Centered_Pentadecagonal_num(n)); } } // This code is contributed by sapnasingh4991 |
Javascript
<script> // Javascript program to find the sum of the // first N centered pentadecagonal number // Function to find the centered // pentadecagonal number function Centered_Pentadecagonal_num(n) { // Formula to calculate // N-th centered pentadecagonal // number return (15 * n * n - 15 * n + 2) / 2; } // Function to find the sum of // the first N centered // pentadecagonal numbers function sum_Centered_Pentadecagonal_num(n) { // Variable to store // the sum let summ = 0; for (let i = 1; i < n + 1; i++) { summ += Centered_Pentadecagonal_num(i); } return summ; } let n = 5; document.write(sum_Centered_Pentadecagonal_num(n)); </script> |
Output:
305
Time Complexity: O(N)
Auxiliary Space: O(1) as it is using constant space for variables