Skip to content
Related Articles

Related Articles

Improve Article

Find the sum of the first Nth Icosidigonal Number

  • Last Updated : 18 Mar, 2021

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 … 
 

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.  To complete your preparation from learning a language to DS Algo and many more,  please refer Complete Interview Preparation Course.

In case you wish to attend live classes with experts, please refer DSA Live Classes for Working Professionals and Competitive Programming Live for Students.

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 <bits/stdc++.h>
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




<script>
    // Javascript program to find the sum of the
    // first N icosidigonal numbers
     
    // Function to find the 
    // N-th icosidigonal number 
    function 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 
    function sum_Icosidigonal_num(n)
    {
 
        // Variable to store the sum
        let summ = 0;
 
        // Iterating in the range 1 to N
        for(let i = 1; i < n + 1; i++)
        {
 
            // Finding the sum
            summ += Icosidigonal_num(i);
        }
        return summ;
    }
     
    let n = 6;
       
    // Display first Nth 
    // icosidigonal numbers
    document.write(sum_Icosidigonal_num(n));
 
// This code is contributed by divyesh072019.
</script>
Output: 
721

 

Time complexity: O(N).
 




My Personal Notes arrow_drop_up
Recommended Articles
Page :