Find the sum of the first N Centered Pentagonal Number
Given a number N, the task is to find the sum of first N Centered Pentagonal Numbers.
The first few Centered Pentagonal Number are 1, 6, 16, 31, 51, 76, 106 …
Examples:
Input: N = 3
Output: 23
Explanation:
1, 6 and 16 are the first three
Centered Pentagonal number.
Input: N = 5
Output: 105
Approach: The idea is to first create a function which would help us to find the centered pentagonal number in a constant time. The implementation of this function has already been discussed in this article. The following steps are followed after creating this function:
- Run a loop starting from 1 to N, to find ith Centered Pentagonal number.
- Add all the above calculated Centered Pentagonal numbers.
- Then, display the sum of N Centered Pentagonal numbers.
Below is the implementation of the above approach:
C++
// C++ program to find the sum of the // first N centered pentagonal numbers #include<bits/stdc++.h> using namespace std; // Function to find the // Centered_Pentagonal number int Centered_Pentagonal_num( int n) { // Formula to calculate // nth Centered_Pentagonal // number & return it // into main function. return (5 * n * n - 5 * n + 2) / 2; } // Function to find the sum of the first // N Centered_Pentagonal numbers int sum_Centered_Pentagonal_num( int n) { // To get the sum int summ = 0; // Iterating through the range // 1 to N for ( int i = 1; i < n + 1; i++) { summ += Centered_Pentagonal_num(i); } return summ; } // Driver Code int main() { int n = 5; // Display first Nth // Centered_Pentagonal number cout << (sum_Centered_Pentagonal_num(n)); return 0; } // This code is contributed by PratikBasu |
Java
// Java program to find the sum of the // first N centered pentagonal numbers class GFG{ // Function to find the // Centered_Pentagonal number static int Centered_Pentagonal_num( int n) { // Formula to calculate // nth Centered_Pentagonal // number & return it // into main function. return ( 5 * n * n - 5 * n + 2 ) / 2 ; } // Function to find the sum of the first // N Centered_Pentagonal numbers static int sum_Centered_Pentagonal_num( int n) { // To get the sum int summ = 0 ; // Iterating through the range // 1 to N for ( int i = 1 ; i < n + 1 ; i++) { summ += Centered_Pentagonal_num(i); } return summ; } // Driver Code public static void main(String[] args) { int n = 5 ; // Display first Nth // Centered_Pentagonal number System.out.print((sum_Centered_Pentagonal_num(n))); } } // This code is contributed by sapnasingh4991 |
Python3
# Python3 program to find the sum of # the first N Centered # Pentagonal number # Function to find the # Centered_Pentagonal number def Centered_Pentagonal_num(n): # Formula to calculate # nth Centered_Pentagonal # number & return it # into main function. return ( 5 * n * n - 5 * n + 2 ) / / 2 # Function to find the # sum of the first N # Centered_Pentagonal # numbers def sum_Centered_Pentagonal_num(n) : # To get the sum summ = 0 for i in range ( 1 , n + 1 ): # Function to get the # Centered_Pentagonal_num summ + = Centered_Pentagonal_num(i) return summ # Driver Code if __name__ = = '__main__' : n = 5 # display first Nth # Centered_Pentagonal number print (sum_Centered_Pentagonal_num(n)) |
C#
// C# program to find the sum of the // first N centered pentagonal numbers using System; class GFG{ // Function to find the // Centered_Pentagonal number static int Centered_Pentagonal_num( int n) { // Formula to calculate // nth Centered_Pentagonal // number & return it // into main function. return (5 * n * n - 5 * n + 2) / 2; } // Function to find the sum of the first // N Centered_Pentagonal numbers static int sum_Centered_Pentagonal_num( int n) { // To get the sum int summ = 0; // Iterating through the range // 1 to N for ( int i = 1; i < n + 1; i++) { summ += Centered_Pentagonal_num(i); } return summ; } // Driver code public static void Main(String[] args) { int n = 5; // Display first Nth // Centered_Pentagonal number Console.Write((sum_Centered_Pentagonal_num(n))); } } // This code is contributed by amal kumar choubey |
Javascript
<script> // Javascript program to find the sum of the // first N centered pentagonal numbers // Function to find the // Centered_Pentagonal number function Centered_Pentagonal_num(n) { // Formula to calculate // nth Centered_Pentagonal // number & return it // into main function. return (5 * n * n - 5 * n + 2) / 2; } // Function to find the sum of the first // N Centered_Pentagonal numbers function sum_Centered_Pentagonal_num(n) { // To get the sum let summ = 0; // Iterating through the range // 1 to N for (let i = 1; i < n + 1; i++) { summ += Centered_Pentagonal_num(i); } return summ; } let n = 5; // Display first Nth // Centered_Pentagonal number document.write(sum_Centered_Pentagonal_num(n)); </script> |
Output:
105
Time Complexity: O(n)
Auxiliary Space: O(1)