中心多边形数

给定数字N ，任务是编写一个程序来查找中心多边形数系列的第N个项：

1, 1, 3, 7, 13, 21, 31, 43, 57…..

例子：

Input: N = 0
Output: 1

Input: N = 3
Output: 7

方法：第N个术语可以形式化为：

Series = 1, 3, 7, 13, 21, 31, 43, 57…… 
Difference = 3-1, 7-3, 13-7, 21-13……………. 
Difference = 2, 4, 6, 8……which is a AP
So nth term of given series 
= 1 + (2, 4, 6, 8 …… (n-1)terms) 
= 1 + (n-1)/2*(2*2+(n-1-1)*2) 
= 1 + (n-1)/2*(4+2n-4) 
= 1 + (n-1)*n 
= n^2 – n + 1 
 

因此，该系列的第N个项为

$n^2 - n + 1$

下面是上述方法的实现：

C++

// C++ program 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 * n - n + 1 << endl;
}
 
// Driver code
int main()
{
    int N = 4;
    findNthTerm(N);
 
    return 0;
}

Java

// Java program 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 * n - n + 1);
}
 
// Driver code
public static void main(String[] args)
{
    int N = 4;
     
    findNthTerm(N);
}
}
 
// This code is contributed by Ritik Bansal

Python3

# Python3 program to find N-th term
# in the series
 
# Function to find N-th term
# in the series
def findNthTerm(n):
    print(n * n - n + 1)
 
# Driver code
N = 4
 
# Function Call
findNthTerm(N)
 
# This code is contributed by Vishal Maurya

C#

// C# program 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 * n - n + 1);
}
 
// Driver code
public static void Main()
{
    int N = 4;
     
    findNthTerm(N);
}
}
 
// This code is contributed by nidhi_biet

Javascript

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

输出：

13