Find the sum of the first N Centered Pentagonal Number

Last Updated : 16 Jul, 2021

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 i^th 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# 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:

Time Complexity: O(n)
Auxiliary Space: O(1)

Find the sum of the first N Centered Pentagonal Number

SHUBHAMSINGH10

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Find the sum of the first N Centered Pentagonal Number

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