# Find the sum of the first Nth Icosidigonal Number

Given a number N, the task is to find the sum of the first N Icosidigonal Numbers.

The first few Icosidigonal numbers are 1, 22, 63, 124, 205, 306 …

Examples:

Input: N = 3
Output: 86
Explanation:
1, 22 and 63 are the first three Icosidigonal numbers.
Input: N = 6
Output: 721

Approach:

1. Initially, we need to create a function which will help us to calculate the Nth icosidigonal number.
2. Now, run a loop starting from 1 to N, to find ith icosidigonal numbers.
3. Add all the above calculated icosidigonal numbers.
4. Finally, display the sum of the first N Icosidigonal numbers.

Below is the implementation of the above approach:

## C++

 `// C++ program to find the sum of the``// first N icosidigonal numbers``#include ``using` `namespace` `std; ` `// Function to find the ``// N-th icosidigonal number ``int` `Icosidigonal_num(``int` `n) ``{``    ` `    ``// Formula to calculate ``    ``// nth icosidigonal number``    ``return` `(20 * n * n - 18 * n) / 2;``}` `// Function to find the sum of the``// first N icosidigonal number ``int` `sum_Icosidigonal_num(``int` `n)``{``    ` `    ``// Variable to store the sum``    ``int` `summ = 0;``    ` `    ``// Iterating in the range 1 to N``    ``for``(``int` `i = 1; i < n + 1; i++)``    ``{``        ` `        ``// Finding the sum``        ``summ += Icosidigonal_num(i);``    ``}``    ``return` `summ;``}` `// Driver code ``int` `main() ``{ ``    ``int` `n = 6;``    ` `    ``// Display first Nth ``    ``// icosidigonal numbers``    ``cout << sum_Icosidigonal_num(n);``} ` `// This code is contributed by coder001`

## Java

 `// Java program to find the sum of the ``// first N icosidigonal numbers ``class` `GFG{``    ` `// Function to find the ``// N-th icosidigonal number ``public` `static` `int` `Icosidigonal_num(``int` `n) ``{ ``        ` `    ``// Formula to calculate ``    ``// nth icosidigonal number ``    ``return` `(``20` `* n * n - ``18` `* n) / ``2``; ``} ``    ` `// Function to find the sum of the ``// first N icosidigonal number ``public` `static` `int` `sum_Icosidigonal_num(``int` `n) ``{ ``        ` `    ``// Variable to store the sum ``    ``int` `summ = ``0``; ``        ` `    ``// Iterating in the range 1 to N ``    ``for``(``int` `i = ``1``; i < n + ``1``; i++) ``    ``{ ` `       ``// Finding the sum ``       ``summ += Icosidigonal_num(i); ``    ``} ``    ``return` `summ; ``} ` `// Driver code    ``public` `static` `void` `main(String[] args)``{``    ``int` `n = ``6``; ``    ` `    ``// Display first Nth ``    ``// icosidigonal numbers ``    ``System.out.println(sum_Icosidigonal_num(n));``}``}` `// This code is contributed by divyeshrabadiya07    `

## Python3

 `# Python3 program to find the ``# sum of the first N  ``# Icosidigonal numbers` `# Function to find the ``# N-th Icosidigonal ``# number ``def` `Icosidigonal_num(n):`` ` `    ``# Formula to calculate  ``    ``# nth Icosidigonal ``    ``# number``    ``return` `(``20` `*` `n ``*` `n ``-``            ``18` `*` `n) ``/``/` `2``    ` `  ` `# Function to find the ``# sum of the first N``# Icosidigonal number ``def` `sum_Icosidigonal_num(n) : ``    ` `    ``# Variable to store``    ``# the sum``    ``summ ``=` `0``    ` `    ``# Iterating in the range ``    ``# 1 to N``    ``for` `i ``in` `range``(``1``, n ``+` `1``):` `        ``summ ``+``=` `Icosidigonal_num(i)``    ` `    ``return` `summ``  ` `# Driver code ``if` `__name__ ``=``=` `'__main__'` `: ``          ` `    ``n ``=` `6``    `  `    ``print``(sum_Icosidigonal_num(n)) `

## C#

 `// C# program to find the sum of the ``// first N icosidigonal numbers ``using` `System;` `class` `GFG{ ``        ` `// Function to find the ``// N-th icosidigonal number ``static` `int` `Icosidigonal_num(``int` `n) ``{ ``            ` `    ``// Formula to calculate ``    ``// nth icosidigonal number ``    ``return` `(20 * n * n - 18 * n) / 2; ``} ``        ` `// Function to find the sum of the ``// first N icosidigonal number ``static` `int` `sum_Icosidigonal_num(``int` `n) ``{ ``            ` `    ``// Variable to store the sum ``    ``int` `summ = 0; ``            ` `    ``// Iterating in the range 1 to N ``    ``for``(``int` `i = 1; i < n + 1; i++) ``    ``{ ``        ` `       ``// Finding the sum ``       ``summ += Icosidigonal_num(i); ``    ``} ``    ``return` `summ; ``} ``    ` `// Driver code ``public` `static` `void` `Main(``string``[] args) ``{ ``    ``int` `n = 6; ``        ` `    ``// Display first Nth ``    ``// icosidigonal numbers ``    ``Console.WriteLine(sum_Icosidigonal_num(n)); ``} ``} ` `// This code is contributed by AnkitRai01`

## Javascript

 ``

Output:
`721`

Time complexity: O(N).

Auxiliary space: O(1) since it is using constant space for variables

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