# Find Nth term of series 1, 4, 15, 72, 420…

• Difficulty Level : Easy
• Last Updated : 14 May, 2021

Given a number N. The task is to write a program to find the Nth term in the below series:

1, 4, 15, 72, 420…

Examples:

```Input: 3
Output: 15
For N = 3, we know that the factorial of 3 is 6
Nth term = 6*(3+2)/2
= 15

Input: 6
Output: 2880
For N = 6, we know that the factorial of 6 is 720
Nth term = 620*(6+2)/2
= 2880```

The idea is to first find the factorial of the given number N, that is N!. Now the N-th term in the above series will be:

N-th term = N! * (N + 2)/2

Below is the implementation of the above approach:

## C++

 `// CPP program to find N-th term of the series:``// 1, 4, 15, 72, 420…``#include ``using` `namespace` `std;` `// Function to find factorial of N``int` `factorial(``int` `N)``{``    ``int` `fact = 1;` `    ``for` `(``int` `i = 1; i <= N; i++)``        ``fact = fact * i;``        ` `    ``// return factorial of N        ``    ``return` `fact;``}` `// calculate Nth term of series``int` `nthTerm(``int` `N)``{``    ``return` `(factorial(N) * (N + 2) / 2);``}` `// Driver Function``int` `main()``{``    ``int` `N = 6;``    ` `    ``cout << nthTerm(N);``    ` `    ``return` `0;``}`

## Java

 `// Java program to find N-th``// term of the series:``// 1, 4, 15, 72, 420``import` `java.util.*;``import` `java.lang.*;``import` `java.io.*;` `class` `GFG``{``    ` `// Function to find factorial of N``static` `int` `factorial(``int` `N)``{``    ``int` `fact = ``1``;` `    ``for` `(``int` `i = ``1``; i <= N; i++)``        ``fact = fact * i;``        ` `    ``// return factorial of N    ``    ``return` `fact;``}` `// calculate Nth term of series``static` `int` `nthTerm(``int` `N)``{``    ``return` `(factorial(N) * (N + ``2``) / ``2``);``}` `// Driver Code``public` `static` `void` `main(String args[])``{``    ``int` `N = ``6``;``    ` `    ``System.out.println(nthTerm(N));``}``}` `// This code is contributed by Subhadeep`

## Python3

 `# Python 3 program to find``# N-th term of the series:``# 1, 4, 15, 72, 420…` `# Function for finding``# factorial of N``def` `factorial(N) :``    ``fact ``=` `1``    ``for` `i ``in` `range``(``1``, N ``+` `1``) :``        ``fact ``=` `fact ``*` `i` `    ``# return factorial of N``    ``return` `fact` `# Function for calculating``# Nth term of series``def` `nthTerm(N) :` `    ``# return nth term``    ``return` `(factorial(N) ``*` `(N ``+` `2``) ``/``/` `2``)` `# Driver code``if` `__name__ ``=``=` `"__main__"` `:``    ` `    ``N ``=` `6` `    ``# Function Calling``    ``print``(nthTerm(N))` `# This code is contributed``# by ANKITRAI1`

## C#

 `// C# program to find N-th``// term of the series:``// 1, 4, 15, 72, 420``using` `System;` `class` `GFG``{``    ` `// Function to find factorial of N``static` `int` `factorial(``int` `N)``{``    ``int` `fact = 1;` `    ``for` `(``int` `i = 1; i <= N; i++)``        ``fact = fact * i;``        ` `    ``// return factorial of N    ``    ``return` `fact;``}` `// calculate Nth term of series``static` `int` `nthTerm(``int` `N)``{``    ``return` `(factorial(N) * (N + 2) / 2);``}` `// Driver Code``public` `static` `void` `Main()``{``    ``int` `N = 6;``    ` `    ``Console.Write(nthTerm(N));``}``}` `// This code is contributed by ChitraNayal`

## PHP

 ``

## Javascript

 ``

Output:

`2880`

Another approach :(Using recursion)

## C++

 `// CPP program to find N-th term of the series:``// 1, 4, 15, 72, 420…``// Using recursion``#include ``using` `namespace` `std;` `// Function to find factorial of N``// with recursion``int` `factorial(``int` `N)``{``    ``// base condition``    ``if``( N == 0 || N == 1 )``        ``return` `1;``    ``// use recursion``    ``return` `N * factorial( N - 1 );``}` `// calculate Nth term of series``int` `nthTerm(``int` `N)``{``    ``return` `(factorial(N) * (N + 2) / 2);``}` `// Driver Function``int` `main()``{``    ``int` `N = 6;``    ` `    ``cout << nthTerm(N);``    ` `    ``return` `0;``}`

## Java

 `// Java program to find N-th``// term of the series:``// 1, 4, 15, 72, 420``import` `java.util.*;``import` `java.lang.*;``import` `java.io.*;` `class` `GFG``{``    ` `// Function to find factorial of N``static` `int` `factorial(``int` `N)``{``    ``// base condition``    ``if``( N == ``0` `|| N == ``1` `)``        ``return` `1``;``    ``// use recursion``    ``return` `N * factorial( N - ``1` `);``}` `// calculate Nth term of series``static` `int` `nthTerm(``int` `N)``{``    ``return` `(factorial(N) * (N + ``2``) / ``2``);``}` `// Driver Code``public` `static` `void` `main(String args[])``{``    ``int` `N = ``6``;``    ` `    ``System.out.println(nthTerm(N));``}``}`

## Python3

 `# Python3 program to find``# N-th term of the series:``# 1, 4, 15, 72, 420…``# Using recursion` `# Function to find factorial``# of N with recursion``def` `factorial(N):` `    ``# base condition``    ``if` `N ``=``=` `0` `or` `N ``=``=` `1``:``        ``return` `1` `    ``# use recursion``    ``return` `N ``*` `factorial(N ``-` `1``)` `def` `nthTerm(N):``    ` `    ``# calculate Nth term of series``    ``return` `(factorial(N) ``*` `(N ``+` `2``) ``/``/` `2``)` `# Driver code``N ``=` `6``print``(nthTerm(N))` `# This code is contributed``# by Shrikant13`

## C#

 `// C# program to find N-th``// term of the series:``// 1, 4, 15, 72, 420``using` `System;` `class` `GFG``{``    ` `// Function to find factorial of N``static` `int` `factorial(``int` `N)``{``    ``// base condition``    ``if``( N == 0 || N == 1 )``        ``return` `1;``    ``// use recursion``    ``return` `N * factorial( N - 1 );``}` `// calculate Nth term of series``static` `int` `nthTerm(``int` `N)``{``    ``return` `(factorial(N) * (N + 2) / 2);``}` `// Driver Code``public` `static` `void` `Main()``{``    ``int` `N = 6;``    ` `    ``Console.Write(nthTerm(N));``}``}` `// This code is contributed by ChitraNayal`

## PHP

 ``

## Javascript

 ``

Output:

`2880`

Time complexity: O(N)
Note: Above code wouldn’t not work for large values of N. To find the values for large N, use the concept of Factorial for large numbers.

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