# Find the sum of the first Nth Icosagonal Numbers

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

The first few Icosagonal numbers are 1, 20, 57, 112, 185, 276…

Examples:

Input: N = 3
Output: 78
Explanation:
1, 20 and 57 are the first three
Icosagonal number.

Input: N = 5
Output: 375

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

Approach:

1. Initially, we need to create a function which will help us to calculate the N-th Icosagonal number.
2. Now, Run a loop starting from 1 to N, to find the sum of all the Icosagonal number.
3. Now, add all the above calculated Icosagonal numbers.
4. Finally, display the sum of 1st N Icosagonal numbers.

Below is the implementation of the above approach:

## C++

 `// C++ program to find the sum of ` `// the first N icosagonal number  ` `#include ` `using` `namespace` `std; ` ` `  `// Function to calculate the  ` `// N-th icosagonal number  ` `int` `Icosagonal_num(``int` `n) ` `{ ` `    ``// Formula to calculate  ` `    ``// nth icosagonal number  ` `    ``// & return it  ` `    ``return` `(18 * n * n - 16 * n) / 2; ` `} ` `     `  `// Function to find the  ` `// sum of the first N  ` `// icosagonal numbers  ` `int` `sum_Icosagonal_num(``int` `n) ` `{ ` `    ``// Variable to store  ` `    ``// the sum  ` `    ``int` `summ = 0; ` `         `  `    ``// Loop to iterate through  ` `    ``// the first N values and  ` `    ``// find the sum of first N  ` `    ``// icosagonal numbers  ` `    ``for``(``int` `i = 1; i <= n; i++) ` `    ``{ ` `         `  `        ``// Function to get the  ` `        ``// Icosagonal_num  ` `        ``summ += Icosagonal_num(i);  ` `    ``} ` `    ``return` `summ; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `n = 5;  ` `     `  `    ``// Display the sum of  ` `    ``// first N icosagonal number  ` `    ``cout << sum_Icosagonal_num(n) << endl; ` `} ` ` `  `// This code is contributed by rutvik_56 `

## Java

 `// Java program to find the sum of ` `// the first N icosagonal number  ` `class` `GFG{ ` `     `  `// Function to calculate the  ` `// N-th icosagonal number  ` `public` `static` `int` `Icosagonal_num(``int` `n) ` `{ ` `     `  `    ``// Formula to calculate  ` `    ``// nth icosagonal number  ` `    ``// & return it  ` `    ``return` `(``18` `* n * n - ``16` `* n) / ``2``; ` `} ` `     `  `// Function to find the  ` `// sum of the first N  ` `// icosagonal numbers  ` `public` `static` `int` `sum_Icosagonal_num(``int` `n) ` `{ ` `     `  `    ``// Variable to store  ` `    ``// the sum  ` `    ``int` `summ = ``0``; ` `         `  `    ``// Loop to iterate through  ` `    ``// the first N values and  ` `    ``// find the sum of first N  ` `    ``// icosagonal numbers  ` `    ``for``(``int` `i = ``1``; i <= n; i++) ` `    ``{ ` `         `  `       ``// Function to get the  ` `       ``// Icosagonal_num  ` `       ``summ += Icosagonal_num(i);  ` `    ``} ` `    ``return` `summ; ` `} ` ` `  `// Driver code ` `public` `static` `void` `main(String[] args) ` `{ ` `    ``int` `n = ``5``;  ` `     `  `    ``// Display the sum of  ` `    ``// first N icosagonal number  ` `    ``System.out.println(sum_Icosagonal_num(n)); ` `} ` `} ` ` `  `// This code is contributed by divyeshrabadiya07         `

## Python3

 `# Python program to find the  ` `# sum of the first N   ` `# Icosagonal number ` ` `  `# Function to calculate the  ` `# N-th Icosagonal number ` `def` `Icosagonal_num(n):  ` ` `  `    ``# Formula to calculate   ` `    ``# nth Icosagonal  ` `    ``# number & return it   ` `    ``return` `(``18` `*` `n ``*` `n ``-`  `            ``16` `*` `n) ``/``/` `2` `     `  `   `  `# Function to find the  ` `# sum of the first N ` `# Icosagonal numbers  ` `def` `sum_Icosagonal_num(n) :  ` `     `  `    ``# Variable to store  ` `    ``# the sum ` `    ``summ ``=` `0` `     `  `    ``# Loop to iterate through ` `    ``# the first N values and  ` `    ``# find the sum of first N ` `    ``# Icosagonal numbers ` `    ``for` `i ``in` `range``(``1``, n ``+` `1``): ` ` `  `        ``# function to get the  ` `        ``# Icosagonal_num  ` `        ``summ ``+``=` `Icosagonal_num(i) ` `     `  `    ``return` `summ ` `   `  `# Driver Code  ` `if` `__name__ ``=``=` `'__main__'` `:  ` `           `  `    ``n ``=` `5` `     `  `    ``# Display the sum of  ` `    ``# first N Icosagonal number ` `    ``print``(sum_Icosagonal_num(n))  `

## C#

 `// C# program to find the sum of ` `// the first N icosagonal number  ` `using` `System; ` ` `  `class` `GFG{ ` `     `  `// Function to calculate the  ` `// N-th icosagonal number  ` `public` `static` `int` `Icosagonal_num(``int` `n) ` `{ ` `     `  `    ``// Formula to calculate  ` `    ``// nth icosagonal number  ` `    ``// & return it  ` `    ``return` `(18 * n * n - 16 * n) / 2; ` `} ` `     `  `// Function to find the  ` `// sum of the first N  ` `// icosagonal numbers  ` `public` `static` `int` `sum_Icosagonal_num(``int` `n) ` `{ ` `     `  `    ``// Variable to store  ` `    ``// the sum  ` `    ``int` `summ = 0; ` `         `  `    ``// Loop to iterate through  ` `    ``// the first N values and  ` `    ``// find the sum of first N  ` `    ``// icosagonal numbers  ` `    ``for``(``int` `i = 1; i <= n; i++) ` `    ``{ ` ` `  `       ``// Function to get the  ` `       ``// Icosagonal_num  ` `       ``summ += Icosagonal_num(i);  ` `    ``} ` `    ``return` `summ; ` `} ` ` `  `// Driver code ` `public` `static` `void` `Main() ` `{ ` `    ``int` `n = 5;  ` `     `  `    ``// Display the sum of  ` `    ``// first N icosagonal number  ` `    ``Console.WriteLine(sum_Icosagonal_num(n)); ` `} ` `} ` ` `  `// This code is contributed by Code_Mech `

Output:

```375
```

Time complexity: O(N)

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