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# Find Nth term of the series 0, 2, 6, 12, 20, 30, 42…

Given a positive integer N, the task is to find the Nth term of the series

0, 2, 6, 12, 20…till N terms

Examples:

Input: N = 7
Output: 42

Input: N = 10
Output: 90

Approach:

From the given series, find the formula for Nth term-

1st term = 1 * (1 – 1) = 0

2nd term = 2 * (2 – 1) = 2

3rd term = 3 * (3 – 1) = 6

4th term = 4 * (4 – 1) = 12

.

.

Nth term = N * (N – 1)

The Nth term of the given series can be generalized as-

TN = N * (N – 1)

Illustration:

Input: N = 7
Output: 42
Explanation:
TN = N * (N – 1)
= 7 * (7 – 1)
= 7 * 6
= 42

Below is the implementation of the above approach-

## C++

 `// C++ program to implement` `// the above approach` `#include ` `using` `namespace` `std;`   `// Function to return` `// Nth term of the series` `int` `nthTerm(``int` `n)` `{` `    ``return` `n * n - n;` `}`   `// Driver code` `int` `main()` `{` `    ``// Value of N` `    ``int` `N = 7;` `    ``cout << nthTerm(N) << endl;` `    ``return` `0;` `}`

## C

 `// C program to implement` `// the above approach` `#include `   `// Function to return` `// Nth term of the series` `int` `nthTerm(``int` `n)` `{` `    ``return` `n * n - n;` `}`   `// Driver code` `int` `main()` `{` `    ``// Value of N` `    ``int` `N = 7;` `    ``printf``(``"%d"``, nthTerm(N));` `    ``return` `0;` `}`

## Java

 `// Java program to implement` `// the above approach` `import` `java.io.*;`   `class` `GFG {` `    ``public` `static` `void` `main(String[] args)` `    ``{` `        ``// Value of N` `        ``int` `N = ``7``;` `        ``System.out.println(nthTerm(N));` `    ``}`   `    ``// Function to return` `    ``// Nth term of the series` `    ``public` `static` `int` `nthTerm(``int` `n)` `    ``{` `        ``return` `n * n - n;` `    ``}` `}`

## Python3

 `# Python code for the above approach `   `# Function to return` `# Nth term of the series` `def` `nthTerm(n):` `    ``return` `n ``*` `n ``-` `n;`   `# Driver code`   `# Value of N` `N ``=` `7``;` `print``(nthTerm(N));`   `# This code is contributed by Saurabh Jaiswal`

## C#

 `using` `System;`   `public` `class` `GFG ` `{`   `  ``// Function to return` `  ``// Nth term of the series` `  ``public` `static` `int` `nthTerm(``int` `n)` `  ``{` `    ``return` `n * n - n;` `  ``}` `  `  `  ``static` `public` `void` `Main()` `  ``{`   `    ``// Code` `    ``// Value of N` `    ``int` `N = 7;` `    ``Console.Write(nthTerm(N));` `  ``}` `}`   `// This code is contributed by Potta Lokesh`

## Javascript

 ``

Output

`42`

Time Complexity: O(1) // since no loop is used the algorithm takes up constant time to perform the operations
Auxiliary Space: O(1) // since no extra array is used so the space taken by the algorithm is constant

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