找出系列1的第N个项2 + 6 + 15 + 31 + 56 +…

给定一个整数$N$ 。任务是编写一个程序来查找给定序列的第N个术语：

1 + 2 + 6 + 15 + 31 + 56 + ... 

例子：

Input : N = 8
Output : 141

Input : N = 20
Output : 2471

方法：
给定的序列是：

1, 2, 6, 15, 31, 56, 92, 141, ...

连续第一个差异：

1 4 9 16 25 36 49 .......

连续第二个差异：

3 5 7 9 11 13......

由于第二个连续差在AP中，所以序列的第n个项(t _n )的形式为
A(n – 1)(n – 2)(n – 3)+ B(n – 1)(n – 2)+ C(n – 1)+ D
因此，t _n = A(n – 1)(n – 2)(n – 3)+ B(n – 1)(n – 2)+ C(n – 1)+ D
现在，
t ₁ = D = 1
t ₂ = C(2-1)+ D = 2
t ₃ = 2B + 2C + D = 6
t ₄ = CA + 6B + 3C + D = 15
在求解上述四个方程式时，我们得到=> A = 1/3，B = 3/2，C = 1，D =1。代入这些值t _n并经过简化，我们得到：
$t_{n} = \frac{2n^{3}-3n^{2}+n+6}{6}$
下面是上述方法的实现：

C++

// C++ program to find Nth
// term of the series:
// 1 + 2 + 6 + 15 + 31 + 56 + ...
#include
#include
using namespace std;
 
// calculate Nth term of given series
int Nth_Term(int n)
{
    return (2 * pow(n, 3) - 3 *
                pow(n, 2) + n + 6) / 6;
}
 
// Driver code
int main()
{
    int N = 8;
    cout << Nth_Term(N);
}

Java

// Java program to find Nth
// term of the series:
// 1 + 2 + 6 + 15 + 31 + 56 + ...
import java.util.*;
import java.lang.*;
 
class GFG
{
// calculate Nth term of given series
static double Nth_Term(int n)
{
    return (2 * Math.pow(n, 3) - 3 *
                Math.pow(n, 2) + n + 6) / 6;
}
 
// Driver code
static public void main (String args[])
{
    int N = 8;
    System.out.println(Nth_Term(N));
}
}
 
// This code is contributed
// by Akanksha Rai

Python3

# Python program to find Nth term of the series:
# 1 + 2 + 6 + 15 + 31 + 56 + ...
 
# calculate Nth term of given series
def Nth_Term(n):
    return (2 * pow(n, 3) - 3 * pow(n, 2) + n + 6) // 6
 
# Driver code
N = 8
print(Nth_Term(N))

C#

// C# program to find Nth
// term of the series:
// 1 + 2 + 6 + 15 + 31 + 56 + ...
using System;
 
class GFG
{
// calculate Nth term of given series
static double Nth_Term(int n)
{
    return (2 * Math.Pow(n, 3) - 3 *
                Math.Pow(n, 2) + n + 6) / 6;
}
 
// Driver code
static public void Main ()
{
    int N = 8;
    Console.WriteLine(Nth_Term(N));
}
}
 
// This code is contributed
// by Sach_Code

Javascript

// js program to find Nth
// term of the series:
// 1 + 2 + 6 + 15 + 31 + 56 + ..
 
// calculate Nth term of given series
function Nth_Term(n)
{
    return (2 * Math.pow(n, 3) - 3 *
                Math.pow(n, 2) + n + 6) / 6;
}
 
// Driver code
let N = 8;
 
document.write(Nth_Term(N));
 
// This code is contributed
// by pulamolu mohan pavan cse

输出：

141