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Find the sum of the first Nth Icosagonal Numbers

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  • Last Updated : 19 Sep, 2022
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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<bits/stdc++.h>
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




<script>
 
    // Javascript program to find the sum of
      // the first N icosagonal number
     
    // Function to calculate the 
    // N-th icosagonal number 
    function 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 
    function sum_Icosagonal_num(n)
    {
        // Variable to store 
        // the sum 
        let summ = 0;
 
        // Loop to iterate through 
        // the first N values and 
        // find the sum of first N 
        // icosagonal numbers 
        for(let i = 1; i <= n; i++)
        {
 
            // Function to get the 
            // Icosagonal_num 
            summ += Icosagonal_num(i); 
        }
        return summ;
    }
       
      let n = 5; 
       
    // Display the sum of 
    // first N icosagonal number
    document.write(sum_Icosagonal_num(n));
     
</script>

Output: 

375

 

Time complexity: O(N)

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


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