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Second heptagonal numbers

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The Second heptagonal numbers series can be represented as  

4, 13, 27, 46, 70, 99, 133, 172, 216, …..

Nth term

Given an integer N. The task is to find the N-th term of the given series.
Examples:  

Input: N = 1 
Output: 4


Input: N = 4 
Output: 46  

Approach: The idea is to find the general term for the Second heptagonal numbers. Below is the computation of the general term for second heptagonal numbers:  

Series = 4, 13, 27, 46, 70, 99, 133, 172, 216, ….. 
Difference = 13-4, 27-13, 46-27, 70-46, ……………. 
Difference = 9, 14, 19, 24……which is a AP
So nth term of given series 
nth term = 4 + (9 + 14 + 19 + 24 …… (n-1)terms) 
nth term = 4 + (n-1)/2*(2*9+(n-1-1)*5) 
nth term = 4 + (n-1)/2*(18+5n-10) 
nth term = 4 + (n-1)*(5n+8)/2 
nth term = n*(5*n+3)/2 
Therefore, the Nth term of the series is given as 

\frac{n*(5*n+3)}{2}

Below is the implementation of above approach:  

C++

// C++ implementation to
// find N-th term in the series
 
#include <iostream>
#include <math.h>
using namespace std;
 
// Function to find N-th term
// in the series
void findNthTerm(int n)
{
    cout << n * (5 * n + 3) / 2
         << endl;
}
 
// Driver code
int main()
{
    int N = 4;
    findNthTerm(N);
 
    return 0;
}

                    

Java

// Java implementation to
// find N-th term in the series
class GFG{
 
// Function to find N-th term
// in the series
static void findNthTerm(int n)
{
    System.out.println(n * (5 * n + 3) / 2);
}
 
// Driver code
public static void main(String[] args)
{
    int N = 4;
     
    findNthTerm(N);
}
}
 
// This code is contributed by Ritik Bansal

                    

Python 3

# Python implementation to
# find N-th term in the series
 
# Function to find N-th term
# in the series
def findNthTerm(n):
    print(n * (5 * n + 3) // 2)
 
# Driver code
N = 4
 
# Function call
findNthTerm(N)
 
# This code is contributed by Vishal Maurya.

                    

C#

// C# implementation to
// find N-th term in the series
using System;
class GFG{
 
// Function to find N-th term
// in the series
static void findNthTerm(int n)
{
    Console.Write(n * (5 * n + 3) / 2);
}
 
// Driver code
public static void Main()
{
    int N = 4;
     
    findNthTerm(N);
}
}
 
// This code is contributed by Code_Mech

                    

Javascript

<script>
// Javascript implementation to
// find N-th term in the series
 
// Function to find N-th term
// in the series
function findNthTerm(n)
{
    document.write(parseInt((n * (5 * n + 3)) / 2));
}
 
// Driver code
let N = 4;
findNthTerm(N);
 
// This code is contributed by rishavmahato348.
</script>

                    

Output: 
46

 

Time Complexity: O(1)

Auxiliary Space: O(1)

Reference:OEIS



Last Updated : 07 Apr, 2021
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