# Find the sum of the first Nth Icosagonal Numbers

• Last Updated : 19 Sep, 2022

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

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`

## Javascript

 ``

Output:

`375`

Time complexity: O(N)

Auxiliary Space: O(1) since constant space for variables is used

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