找到系列 3,10,21,36,55... 的第 N 项

给定一个正整数N ，任务是找到序列的第 N项

3, 10, 21, 36, 55…till N terms

例子：

Input: N = 4
Output: 36

Input: N = 6
Output: 78

方法：

从给定的系列中，找到第 N项的公式-

1st term = 1 * ( 2(1) + 1 ) = 3

2nd term = 2 * ( 2(2) + 1 ) = 10

3rd term = 3 * ( 2(3) + 1 ) = 21

4th term = 4 * ( 2(4) + 1 ) = 36

.

.

Nth term = N * ( 2(N) + 1 ) 

给定系列的第 N 项可以概括为-

T_N =  N * ( 2(N) + 1 ) 

插图：

Input: N = 10
Output: 210
Explanation: 
T_N = N * ( 2(N) + 1 )  
     = 10 * ( 2(10) + 1 ) 
     = 210

以下是上述方法的实现 -

C++

// C++ program to implement
// the above approach
#include 
using namespace std;
 
// Function to return
// Nth term of the series
int nTh(int n)
{
    return n * (2 * n + 1);
}
 
// Driver code
int main()
{
    int N = 10;
    cout << nTh(N) << endl;
    return 0;
}

C

// C program to implement
// the above approach
#include 
 
// Function to return
// Nth term of the series
int nTh(int n)
{
    return n * (2 * n + 1);
}
 
// Driver code
int main()
{
    // Value of N
    int N = 10;
    printf("%d", nTh(N));
    return 0;
}

Java

// Java program to implement
// the above approach
import java.io.*;
 
class GFG {
    // Driver code
    public static void main(String[] args)
    {
        int N = 10;
        System.out.println(nTh(N));
    }
 
    // Function to return
    // Nth term of the series
    public static int nTh(int n)
    {
        return n * (2 * n + 1);
    }
}

Python

# Python program to implement
# the above approach
 
# Function to return
# Nth term of the series
def nTh(n):
     
    return n * (2 * n + 1)
     
# Driver code
 
N = 10
print(nTh(N))
 
# This code is contributed by Samim Hossain Mondal.

C#

using System;
 
public class GFG
{
 
  // Function to return
  // Nth term of the series
  public static int nTh(int n)
  {
    return n * (2 * n + 1);
  }
  static public void Main (){
 
    // Code
    int N = 10;
    Console.Write(nTh(N));
  }
}
 
// This code is contributed by Potta Lokesh

Javascript

    // JavaScript code for the above approach
 
    // Function to return
    // Nth term of the series
    function nTh(n) {
        return n * (2 * n + 1);
    }
 
    // Driver code
    let N = 10;
    document.write(nTh(N) + '<br>');
 
   // This code is contributed by Potta Lokesh

输出

210

时间复杂度： O(1)

辅助空间： O(1)