五角形第二个数字

第二个五边形数字是对象的集合，可以以规则五边形的形式排列。
五角形的第二个系列是：

2, 7, 15, 26, 40, 57, 77, 100, 126, …..

查找第二个五角形系列的^第N^个项

给定整数N。任务是找到第二个五边形级数的第N个项。
例子：

Input: N = 1 
Output: 2
Input: N = 4 
Output: 26 
 

方法：想法是找到可以通过以下观察得出的系列的通用术语：

Series = 2, 7, 15, 26, 40, 57, 77, 100, 126, …..
Difference = 7 – 2, 15 – 7, 26 – 15, 40 – 26, ……………. 
= 5, 8, 11, 14……which is an AP
So nth term of given series 
nth term = 2 + (5 + 8 + 11 + 14 …… (n-1)terms) 
= 2 + (n-1)/2*(2*5+(n-1-1)*3) 
= 2 + (n-1)/2*(10+3n-6) 
= 2 + (n-1)*(3n+4)/2 
= n*(3*n + 1)/2 
 

因此，该系列的第N个项为$\frac{n*(3*n+1)}{2}$
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 * (3 * n + 1) / 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.print(n * (3 *
                     n + 1) / 2 + "\n");
}
 
// Driver code
public static void main(String[] args)
{
    int N = 4;
    findNthTerm(N);
}
}
 
// This code is contributed by 29AjayKumar

Python3

# Python3 implementation to
# find N-th term in the series
 
# Function to find N-th term
# in the series
def findNthTerm(n):
 
    print(n * (3 * n + 1) // 2, end = " ");
 
# Driver code
N = 4;
findNthTerm(N);
 
# This code is contributed by Code_Mech

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 * (3 *
                  n + 1) / 2 + "\n");
}
 
// Driver code
public static void Main()
{
    int N = 4;
    findNthTerm(N);
}
}
 
// This code is contributed by Code_Mech

Javascript

 
// Javascript implementation t
// find N-th term in the series
 
// Function to find N-th term
// in the series
function findNthTerm(n)
{
    document.write(n * (3 * n + 1) / 2);
}
 
// Driver code
N = 4;
findNthTerm(N);
 

输出：

26

参考： https : //oeis.org/A005449