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120-gon number
  • Last Updated : 16 Mar, 2021
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Given a number N, the task is to find Nth 120-gon number.
 

A 120-gon number is a class of figurate numbers. It has 120 – sided polygon called 120-gon. The N-th 120-gon number count’s the 120 number of dots and all other dots are surrounding with a common sharing corner and make a pattern. The first few 120-gon numbers are 1, 120, 357, 712, 1185, 1776, … 
 

Examples: 
 

Input: N = 2 
Output: 120 
Explanation: 
The second 120-gonol number is 120. 
Input: N = 3 
Output: 357 
 

 



Approach: The N-th 120-gon number is given by the formula:
 

  • Nth term of s sided polygon = \frac{((s-2)n^2 - (s-4)n)}{2}
     
  • Therefore Nth term of 120 sided polygon is
     

Tn =\frac{((120-2)n^2 - (120-4)n)}{2} =\frac{(118^2 - 116)}{2}

  •  

Below is the implementation of the above approach:
 

C++




// C++ implementation for above approach
#include <bits/stdc++.h>
using namespace std;
 
// Function to find the 
// nth 120-gon Number
int gonNum120(int n)
{
    return (118 * n * n - 116 * n) / 2;
}
 
// Driver Code
int main()
{
    int n = 3;
    cout << gonNum120(n);
 
    return 0;
}

Java




// Java program for above approach
class GFG{
 
// Function to find the
// nth 120-gon Number
static int gonNum120(int n)
{
    return (118 * n * n - 116 * n) / 2;
}
 
// Driver code
public static void main(String[] args)
{
    int n = 3;
    System.out.print(gonNum120(n));
}
}
 
// This code is contributed by shubham

Python3




# Python3 implementation for above approach
 
# Function to find the
# nth 120-gon Number
def gonNum120(n):
 
    return (118 * n * n - 116 * n) // 2;
 
# Driver Code
n = 3;
print(gonNum120(n));
 
# This code is contributed by Code_Mech

C#




// C# program for above approach
using System;
class GFG{
 
// Function to find the
// nth 120-gon Number
static int gonNum120(int n)
{
    return (118 * n * n - 116 * n) / 2;
}
 
// Driver code
public static void Main(String[] args)
{
    int n = 3;
    Console.Write(gonNum120(n));
}
}
 
// This code is contributed by sapnasingh4991

Javascript




<script>
 
// JavaScript implementation for above approach
 
// Function to find the 
// nth 120-gon Number
function gonNum120(n)
{
    return (118 * n * n - 116 * n) / 2;
}
 
// Driver Code
var n = 3;
document.write(gonNum120(n));
 
 
</script>
Output: 
357

 

Reference: https://en.wikipedia.org/wiki/120-gon

 

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