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++ 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 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 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 |
<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> |
105
Time Complexity: O(n)
Auxiliary Space: O(1)