第二个七边形数

第二个七边形数字系列可以表示为

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

第N个学期

给定整数N。任务是找到给定级数的第N个项。
例子：

Input: N = 1 
Output: 4

Input: N = 4 
Output: 46  

方法：想法是找到第二个七边形数字的总称。下面是第二个七边形数字的通用术语的计算：

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 

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

下面是上述方法的实现：

C++

// C++ implementation to
// find N-th term in the series
 
#include 
#include 
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

// 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.

输出：

46

时间复杂度： O(1)

辅助空间： O(1)

参考： OEIS