Find the Nth term of the series 1, 2, 6, 21, 88, 445. . .

Given a positive integer N. The task is to find Nth term of the series:

1, 2, 6, 21, 88, 445, . . .

Examples:

Input: N = 3
Output: 6

Input: N = 6
Output: 445

Approach:

The given sequence follows the following pattern-

1, (1 * 1 + 1 = 2), (2 * 2 + 2 = 6), (6 * 3 + 3 = 21), (21 * 4 + 4 = 88), (88 * 5 + 5 = 445), … 

Below steps can be used to solve the problem-

• For each iterative i, multiplying its previous element with i (Initially the element will be 1)
• And add multiplied elements with i.
• Finally, return the Nth term of the series.

Below is the implementation of the above approach

C++

// C++ program to find N-th term
// of the series-
// 1, 2, 6, 21, 88, 445...
#include <bits/stdc++.h>
using namespace std;

// Function to return Nth term
// of the series
int nthTerm(int N)
{
    // Initializing a variable
    int term = 1;

    // Loop to iterate from 1 to N-1
    for (int i = 1; i < N; i++)
    {
        // Multiplying and adding previous
        // element with i
        term = term * i + i;
    }

    // returning the Nth term
    return term;
}

// Driver Code
int main()
{
    // Get the value of N
    int N = 6;
    cout << nthTerm(N);
    return 0;
}

Java

// Java program to find N-th term
// of the series-
// 1, 2, 6, 21, 88, 445...
class GFG
{

    // Function to return Nth term
    // of the series
    static int nthTerm(int N)
    {

        // Initializing a variable
        int term = 1;

        // Loop to iterate from 1 to N-1
        for (int i = 1; i < N; i++)
        {

            // Multiplying and adding previous
            // element with i
            term = term * i + i;
        }

        // returning the Nth term
        return term;
    }

    // Driver Code
    public static void main(String args[])
    {

        // Get the value of N
        int N = 6;
        System.out.println(nthTerm(N));
    }

}

// This code is contributed by saurabh_jaiswal.

Python3

# Python code for the above approach

# Function to return Nth term
# of the series
def nthTerm(N):

    # Initializing a variable
    term = 1;

    # Loop to iterate from 1 to N-1
    for i in range(1, N):

        # Multiplying and adding previous
        # element with i
        term = term * i + i;

    # returning the Nth term
    return term;

# Driver Code

# Get the value of N
N = 6;
print(nthTerm(N));

# This code is contributed by Saurabh Jaiswal

C#

// C# program to find N-th term
// of the series-
// 1, 2, 6, 21, 88, 445...
using System;
class GFG
{

  // Function to return Nth term
  // of the series
  static int nthTerm(int N)
  {

    // Initializing a variable
    int term = 1;

    // Loop to iterate from 1 to N-1
    for (int i = 1; i < N; i++)
    {

      // Multiplying and adding previous
      // element with i
      term = term * i + i;
    }

    // returning the Nth term
    return term;
  }

  // Driver Code
  public static void Main()
  {

    // Get the value of N
    int N = 6;
    Console.Write(nthTerm(N));
  }

}

// This code is contributed by Samim Hossain Mondal.

Javascript

<script>
        // JavaScript code for the above approach

        // Function to return Nth term
        // of the series
        function nthTerm(N)
        {

            // Initializing a variable
            let term = 1;

            // Loop to iterate from 1 to N-1
            for (let i = 1; i < N; i++)
            {

                // Multiplying and adding previous
                // element with i
                term = term * i + i;
            }

            // returning the Nth term
            return term;
        }

        // Driver Code

        // Get the value of N
        let N = 6;
        document.write(nthTerm(N));

  // This code is contributed by Potta Lokesh
    </script>

Output

445

Time Complexity: O(N)

Auxiliary Space: O(1)