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Find the sum of the first N Centered Pentagonal Number
• Last Updated : 17 Mar, 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:

1. Run a loop starting from 1 to N, to find ith Centered Pentagonal number.
2. Add all the above calculated Centered Pentagonal numbers.
3. Then, display the sum of N Centered Pentagonalnumbers.

Below is the implementation of the above approach:

## C++

 `// C++ program to find the sum of the``// first N centered pentagonal numbers``#include``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

 ``
Output:
`105`

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