# 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

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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 `

Output:

```105
```

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