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# Find N-th term in the series 0, 4, 18, 48, 100 …

• Last Updated : 06 Dec, 2021

Given a series 0, 4, 18, 48, 100 . . .  and an integer N, the task is to find the N-th term of the series.

Examples:

Input: N = 4
Output: 48
Explanation: As given in the sequence we can see that 4th term is 48

Input: N = 6
Output: 180

Approach: Consider the below observation:

For N = 2, the 2nd term is 4, which can be represented as 8 – 4, i.e. 23 – 22

For N = 3, the 3rd term is 18, which can be represented as 27 – 9, i.e. 33 – 32

For N = 4, the 4th term is 18, which can be represented as 27 – 9, i.e. 43 – 42

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Similarly, The N-th term of this series can be represented as N3 – N2

So for any N, find the square of that N and subtract it from the cube of the number.

Below is the implementation of the above approach:

## C++

 `// C++ code to find Nth term of series ` `// 0, 4, 18, ... ` ` `  `#include ` `using` `namespace` `std; ` ` `  `// Function to find N-th term ` `// of the series ` `int` `getNthTerm(``int` `N) ` `{ ` `    ``// (pow(N, 3) - pow(N, 2)) ` `    ``return` `(N * N * N) - (N * N); ` `} ` ` `  `// Driver Code ` `int` `main() ` `{ ` `    ``int` `N = 4; ` ` `  `    ``// Get the 8th term of the series ` `    ``cout << getNthTerm(N); ` `    ``return` `0; ` `}`

## Java

 `// Java code to find Nth term of series ` `// 0, 4, 18, ... ` `class` `GFG ` `{ ` `   `  `    ``// Function to find N-th term ` `    ``// of the series ` `    ``public` `static` `int` `getNthTerm(``int` `N)  ` `    ``{ ` `       `  `        ``// (pow(N, 3) - pow(N, 2)) ` `        ``return` `(N * N * N) - (N * N); ` `    ``} ` ` `  `    ``// Driver Code ` `    ``public` `static` `void` `main(String args[]) ` `    ``{ ` `        ``int` `N = ``4``; ` ` `  `        ``// Get the 8th term of the series ` `        ``System.out.println(getNthTerm(N)); ` `    ``} ` `} ` ` `  `// This code is contributed by gfgking`

## Python3

 `# Python code to find Nth term of series ` `# 0, 4, 18, ... ` ` `  `# Function to find N-th term ` `# of the series ` `def` `getNthTerm(N): ` `   `  `    ``# (pow(N, 3) - pow(N, 2)) ` `    ``return` `(N ``*` `N ``*` `N) ``-` `(N ``*` `N); ` ` `  `# Driver Code ` `N ``=` `4``; ` ` `  `# Get the 8th term of the series ` `print``(getNthTerm(N)); ` ` `  `# This code is contributed by gfgking `

## C#

 `// C# code to find Nth term of series ` `// 0, 4, 18, ... ` ` `  `using` `System; ` `class` `GFG { ` `    ``// Function to find N-th term ` `    ``// of the series ` `    ``public` `static` `int` `getNthTerm(``int` `N) { ` `        ``// (pow(N, 3) - pow(N, 2)) ` `        ``return` `(N * N * N) - (N * N); ` `    ``} ` ` `  `    ``// Driver Code ` `    ``public` `static` `void` `Main() { ` `        ``int` `N = 4; ` ` `  `        ``// Get the 8th term of the series ` `        ``Console.Write(getNthTerm(N)); ` `    ``} ` `} ` ` `  `// This code is contributed by gfgking`

## Javascript

 ``

Output

`48`

Time complexity: O(1)
Auxiliary space: O(1)

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