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Find the sum of the first Nth Centered Pentadecagonal Number
• Last Updated : 17 Mar, 2021

Given a number N the task is to find the sum of the first N Centered Pentadecagonal Number.

The first few Centered Pentadecagonal Numbers are 1, 16, 46, 91, 151, 226, 316 …

Examples:

Input: N = 3
Output: 63
Explanation:
1, 16 and 46 are the first three centered pentadecagonal numbers.
Input: N = 5
Output: 305

Approach:

1. Initially, we need to create a function which will help us to calculate the Nth centred Pentadecagonal number.

2. Now, run a loop starting from 1 to N, to find ith Centered Pentadecagonal number.
4. Finally, display the sum of 1st N Centered Pentadecagonal numbers.

Below is the implementation of the above approach:

## C++

 `// C++ program to find the sum of the``// first N centered pentadecagonal number``#include``using` `namespace` `std;` `// Function to find the centered``// pentadecagonal number``int` `Centered_Pentadecagonal_num(``int` `n)``{` `    ``// Formula to calculate``    ``// N-th centered pentadecagonal``    ``// number``    ``return` `(15 * n * n - 15 * n + 2) / 2;``}` `// Function to find the sum of``// the first N centered``// pentadecagonal numbers``int` `sum_Centered_Pentadecagonal_num(``int` `n)``{` `    ``// Variable to store``    ``// the sum``    ``int` `summ = 0;` `    ``for``(``int` `i = 1; i < n + 1; i++)``    ``{``       ``summ += Centered_Pentadecagonal_num(i);``    ``}``    ``return` `summ;``}` `// Driver Code``int` `main()``{``    ``int` `n = 5;``    ` `    ``cout << sum_Centered_Pentadecagonal_num(n);``    ``return` `0;``}` `// This code is contributed by Rajput-Ji`

## Java

 `// Java program to find the sum of the``// first N centered pentadecagonal number``class` `GFG {``    ` `// Function to find the centered``// pentadecagonal number``static` `int` `Centered_Pentadecagonal_num(``int` `n)``{` `    ``// Formula to calculate``    ``// N-th centered pentadecagonal``    ``// number``    ``return` `(``15` `* n * n - ``15` `* n + ``2``) / ``2``;``}` `// Function to find the sum of``// the first N centered``// pentadecagonal numbers``static` `int` `sum_Centered_Pentadecagonal_num(``int` `n)``{` `    ``// Variable to store``    ``// the sum``    ``int` `summ = ``0``;` `    ``for``(``int` `i = ``1``; i < n + ``1``; i++)``    ``{``       ``summ += Centered_Pentadecagonal_num(i);``    ``}``    ``return` `summ;``}` `// Driver Code``public` `static` `void` `main(String[] args)``{``    ``int` `n = ``5``;` `    ``System.out.println(sum_Centered_Pentadecagonal_num(n));``}``}` `// This code is contributed by sapnasingh4991`

## Python3

 `# Python3 program to find the sum``# of the first N centered ``# Pentadecagonal number` `# Function to find the``# Centered_Pentadecagonal``# number``def` `Centered_Pentadecagonal_num(n):` `    ``# Formula to calculate ``    ``# N-th Centered_Pentadecagonal``    ``# number``    ``return` `(``15` `*` `n ``*` `n ``-``            ``15` `*` `n ``+` `2``) ``/``/` `2``    ` `  ` `# Function to find the``# sum of the first N``# Centered_Pentadecagonal``# numbers``def` `sum_Centered_Pentadecagonal_num(n) :``    ` `    ``# Variable to store``    ``# the sum``    ``summ ``=` `0``    ` `    ``for` `i ``in` `range``(``1``, n ``+` `1``):` `        ``summ ``+``=` `Centered_Pentadecagonal_num(i)``    ` `    ``return` `summ``  ` `# Driver code``if` `__name__ ``=``=` `'__main__'` `:``          ` `    ``n ``=` `5` `    ``print``(sum_Centered_Pentadecagonal_num(n))`

## C#

 `// C# program to find the sum of the``// first N centered pentadecagonal number``using` `System;` `class` `GFG``{``    ` `// Function to find the centered``// pentadecagonal number``static` `int` `Centered_Pentadecagonal_num(``int` `n)``{` `    ``// Formula to calculate``    ``// N-th centered pentadecagonal``    ``// number``    ``return` `(15 * n * n - 15 * n + 2) / 2;``}` `// Function to find the sum of``// the first N centered``// pentadecagonal numbers``static` `int` `sum_Centered_Pentadecagonal_num(``int` `n)``{` `    ``// Variable to store``    ``// the sum``    ``int` `summ = 0;``    ` `    ``for``(``int` `i = 1; i < n + 1; i++)``    ``{``        ``summ += Centered_Pentadecagonal_num(i);``    ``}``    ``return` `summ;``}` `// Driver Code``public` `static` `void` `Main(String[] args)``{``    ``int` `n = 5;` `    ``Console.WriteLine(sum_Centered_Pentadecagonal_num(n));``}``}` `// This code is contributed by sapnasingh4991`

## Javascript

 ``
Output:
`305`

Time Complexity: O(N)

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