找出系列3、9、21、41、71的n个项…

给定数学级数为3、9、21、41、71…对于给定的整数n，必须找到该级数的第n个数字。
例子 ：

Input : n = 4 
Output : 41

Input : n = 2
Output : 9

解决这个问题的首要任务是破解该系列。如果你介绍了一系列仔细一看，对于一般的n个项的值将是^{(σN2)+(σN)+1，}其中

• ^(ΣN2)：是第一n个自然数的平方和。
• (Σn) ：是前n个自然数的总和。
• 1是一个简单的常数值。

因此，为了计算给定级数的第n个项，我们说f(n)有：
^{F(N)=(ΣN2)+(σN)+1}
=((((n *(n + 1)*(2n + 1))/ 6)+(n *(n + 1)/ 2)+ 1
=(n ³ + 3n ² + 2n + 3)/ 3

C++

// Program to calculate
// nth term of a series
#include 
using namespace std;
 
// func for calualtion
int seriesFunc(int n)
{
    // for summation of square
    // of first n-natural nos.
    int sumSquare = (n * (n + 1)
                  * (2 * n + 1)) / 6;
 
    // summation of first n natural nos.
    int sumNatural = (n * (n + 1) / 2);
 
    // return result
    return (sumSquare + sumNatural + 1);
}
 
// Driver Code
int main()
{
    int n = 8;   
    cout << seriesFunc(n) << endl;
     
    n = 13;
    cout << seriesFunc(13);
     
    return 0;
}

Java

// Java Program to calculate
// nth term of a series
import java.io.*;
 
class GFG
{
    // func for calualtion
    static int seriesFunc(int n)
    {
        // for summation of square
        // of first n-natural nos.
        int sumSquare = (n * (n + 1)
                        * (2 * n + 1)) / 6;
     
        // summation of first n natural nos.
        int sumNatural = (n * (n + 1) / 2);
     
        // return result
        return (sumSquare + sumNatural + 1);
    }
     
    // Driver Code
    public static void main(String args[])
    {
        int n = 8;
        System.out.println(seriesFunc(n));
         
        n = 13;
        System.out.println(seriesFunc(13));
    }
}
 
// This code is contributed by Nikita Tiwari.

Python3

# Program to calculate
# nth term of a series
 
# func for calualtion
def seriesFunc(n):
 
    # for summation of square
    # of first n-natural nos.
    sumSquare = (n * (n + 1) *
                (2 * n + 1)) / 6
 
    # summation of first n
    # natural nos.
    sumNatural = (n * (n + 1) / 2)
 
    # return result
    return (sumSquare + sumNatural + 1)
 
# Driver Code
n = 8
print (int(seriesFunc(n)))
 
n = 13
print (int(seriesFunc(n)))
 
# This is code is contributed by Shreyanshi Arun.

C#

// C# program to calculate
// nth term of a series
using System;
 
class GFG
{
    // Function for calualtion
    static int seriesFunc(int n)
    {
        // For summation of square
        // of first n-natural nos.
        int sumSquare = (n * (n + 1)
                        * (2 * n + 1)) / 6;
     
        // summation of first n natural nos.
        int sumNatural = (n * (n + 1) / 2);
     
        // return result
        return (sumSquare + sumNatural + 1);
    }
     
    // Driver Code
    public static void Main()
    {
        int n = 8;
        Console.WriteLine(seriesFunc(n));
         
        n = 13;
        Console.WriteLine(seriesFunc(13));
    }
}
 
// This code is contributed by vt_m.

Javascript

 
// JavaScript Program to calculate
// nth term of a series
 
    // func for calualtion
    function seriesFunc(n)
    {
        // for summation of square
        // of first n-natural nos.
        let sumSquare = (n * (n + 1)
                        * (2 * n + 1)) / 6;
       
        // summation of first n natural nos.
        let sumNatural = (n * (n + 1) / 2);
       
        // return result
        return (sumSquare + sumNatural + 1);
    }
  
// Driver code
 
        let n = 8;
        document.write(seriesFunc(n) + "<br/>");
           
        n = 13;
        document.write(seriesFunc(13));
 

输出 ：

241
911