程序查找系列7、21、49、91、147、217，……的N个术语

给定数字N。任务是编写一个程序来查找以下系列的第N个术语：

7, 21, 49, 91, 147, 217, 301, 399, …(N Terms)

例子：

Input: N = 4
Output: 91
For N = 4
4th Term = ( 7 * 4 * 4 - 7 * 4 + 7) 
         = 91

Input: N = 10
Output: 636

给定的序列是：

7, 21, 49, 91, 147, 217, 301, 399, …..

从所有条款中选择7个共同点，我们得到：

7 * (1, 3, 7, 13, 21, 31,…..), ….. 
 

现在，对于内部系列： 1,3,7,13,21，…
经过仔细观察，我们可以将上述系列的术语表示为：
1 =(1 ² )–(1-1)
3 =(2 ² )–(2-1)
7 =(3 ² )–(3-1)
13 =(4 ² )–(4-1)
21 =(5 ² )–(5-1)
。
。
。
第n个项=(n ² )–(n-1)
因此，实际系列的第n个项将是：

N-th term = 7 * ((n2) - (n-1))
          = 7 * (n2 - n + 1)

下面是上述方法的实现：

C++

// C++ program to find the N-th term of the series:
// 7, 21, 49, 91, 146, 217, 301, 399, ...
#include 
#include 
using namespace std;
 
// calculate Nth term of series
int nthTerm(int n)
{
    return 7 * pow(n, 2) - 7 * n + 7;
}
 
// Driver code
int main()
{
    int N = 4;
 
    cout << nthTerm(N);
 
    return 0;
}

Java

// Java program to find the N-th term of the series:
// 7, 21, 49, 91, 146, 217, 301, 399, ...
 
// calculate Nth term of series
import java.util.*;
 
class solution
{
 
//Function to find the nth term of the series
static int nthTerm(int n)
{
    return 7 * (int)Math.pow(n, 2) - 7 * n + 7;
}
 
// Driver code
public static void main(String arr[])
{
    int N = 4;
 
    System.out.println(nthTerm(N));
 
}
 
}

Python3

# Python3 program to find the N-th term of the series:
# 7, 21, 49, 91, 146, 217, 301, 399, ...
 
 
# calculate Nth term of series
def nthTerm( n):
 
    return 7 * pow(n, 2) - 7 * n + 7
 
 
# Driver code
N = 4
 
print(nthTerm(N))

C#

// C# program to find the
// N-th term of the series:
// 7, 21, 49, 91, 146, 217, 301, 399, ...
using System;
 
// calculate Nth term of series
class GFG
{
 
// Function to find the Nth
// term of the series
static int nthTerm(int n)
{
    return 7 * (int)Math.Pow(n, 2) - 7 * n + 7;
}
 
// Driver code
public static void Main()
{
    int N = 4;
 
    Console.WriteLine(nthTerm(N));
}
}
 
// This code is contributed
// by Akanksha Rai

Javascript

 
// Javascript program to find the N-th term
// of the series:
// 7, 21, 49, 91, 146, 217, 301, 399, ...
 
// Calculate Nth term of series
function nthTerm(n)
{
    return 7 * Math.pow(n, 2) - 7 * n + 7;
}
 
// Driver code
let N = 4;
 
document.write(nthTerm(N));
 
// This code is contributed by Surbhi Tyagi.
 

输出：

91

时间复杂度： O(1)