程序来找到系列3、7、13、21、31…..的第N个术语。

给定数字N，任务是找到该系列的第N个项：

3, 7, 13, 21, 31, …….

例子：

Input: N = 4
Output: 21
Explanation:
Nth term = (pow(N, 2) + N + 1)
         = (pow(4, 2) + 4 + 1)
         = 21

Input: N = 11
Output: 133

方法：
$Sum = 0+3+7+13+21+31+........+a_{n-1} + a_n\\ Sum = 3+7+13+21+31+...+a_{n-2}+a_{n-1}+a_n$
减去这两个方程，我们得到
$$ 0=3+\left \{\frac{n-1}{2}\right \}[2*4 + (n-2)*2]-a_n\\ =3+\left \{\frac{n-1}{2}\right \}[8 + 2n-4]-a_n\\ =3+\left \{\frac{n-1}{2}\right \}[2n+4]-a_n\\ a_n=3+(n-1)(n+2)\\ a_n=n^2+n+1 $$
因此，给定系列的第N个项是：

$a_n=n^2+n+1$

下面是上述方法的实现：

C++

// CPP program to find the Nth term of given series.
#include 
#include 
using namespace std;
 
// Function to calculate sum
long long int getNthTerm(long long int N)
{
    // Return Nth term
    return (pow(N, 2) + N + 1);
}
 
// driver code
int main()
{
    // declaration of number of terms
    long long int N = 11;
 
    // Get the Nth term
    cout << getNthTerm(N);
 
    return 0;
}

Java

// Java code to find the Nth term of given series.
import java.util.*;
 
class solution
{
 
// Function to calculate sum
static long getNthTerm(long N)
{
     
   // Return Nth term
    return ((int)Math.pow(N, 2) + N + 1);
}
 
//Driver program
public static void main(String arr[])
{
     
   // declaration of number of terms
    long N = 11;
 
    // Get the Nth term
    System.out.println(getNthTerm(N));
 
}
}
//THis code is contibuted by
//Surendra_Gangwar

Python3

# Python3 Code to find the
# Nth term of given series.
 
# Function to calculate sum
def getNthTerm(N):
     
    # Return Nth term
    return (pow(N, 2) + N + 1)
 
# driver code
if __name__=='__main__':
     
# declaration of number of terms
    N = 11
     
# Get the Nth term
    print(getNthTerm(N))
 
# This code is contributed by
# Sanjit_Prasad

C#

// C# code to find the Nth
// term of given series.
using System;
 
class GFG
{
 
// Function to calculate sum
static long getNthTerm(long N)
{
     
// Return Nth term
    return ((int)Math.Pow(N, 2) + N + 1);
}
 
// Driver Code
static public void Main ()
{
     
    // declaration of number
    // of terms
    long N = 11;
 
    // Get the Nth term
    Console.Write(getNthTerm(N));
}
}
 
// This code is contibuted by Raj

Javascript

// JavaScript program to find the Nth term of given series.
 
// Function to calculate sum
function getNthTerm(N)
{
    // Return Nth term
    return (Math.pow(N, 2) + N + 1);
}
   
// driver code
 
   // declaration of number of terms
   let N = 11;
   
   // Get the Nth term
   document.write(getNthTerm(N));
   
// This code is contributed by Surbhi Tyagi
 

输出：

133

时间复杂度： O(1)