求数列 1 + 2 + 6 + 15 + 31 + 56 +的第 n 项……

原文:https://www . geesforgeks . org/find-the-n-term-of-series-1-2-6-15-31-56/

给定一个整数N 。任务是编写一个程序来找到给定系列的第 N 个术语:

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

示例 :

Input : N = 8
Output : 141

Input : N = 20
Output : 2471

进场: 给定的系列是:

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

第一个连续差 :

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

第二个连续差 :

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

由于第二个连续的差异是在 AP 中，系列的第 n 项(t n )是这样的形式， A(n–1)(n–2)(n–3)+B(n–1)(n–2)+C(n–1)+D 所以，tn= A(n–1)(n–2)(n–3)+B(n–1)(n–2)+C(n–1)+D 现在， t1= D = 1 t2= C(2–1)+D = 2 t3= 2B+2C+D = 6 t4= CA+6B+3C+D = 15 通过求解上述四个方程，我们得到= > A = 1/3，B = 3/2，C = 1，D = 1。 在将这些值 t n 代入并简化后，我们得到 t_{n} = \frac{2n^{3}-3n^{2}+n+6}{6} 以下是上述方法的实现:

C++

// C++ program to find Nth
// term of the series:
// 1 + 2 + 6 + 15 + 31 + 56 + ...
#include<iostream>
#include<math.h>
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 语言(一种计算机语言，尤用于创建网站)

// 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

Python 3

# 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

服务器端编程语言（Professional Hypertext Preprocessor 的缩写）

<?php
// PHP program to find Nth
// term of the series:
// 1 + 2 + 6 + 15 + 31 + 56 + ..

// calculate Nth term of given series
function Nth_Term($n)
{
    return (2 * pow($n, 3) - 3 *
                pow($n, 2) + $n + 6) / 6;
}

// Driver code
$N = 8;

echo Nth_Term($N);

// This code is contributed by
// Shashank_Sharma
?>

java 描述语言

<script>
// 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
</script>

Output: 

141

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