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# Find the Nth term of the series 3,10,21,36,55…

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

3, 10, 21, 36, 55…till N terms

Examples:

Input: N = 4
Output: 36

Input: N = 6
Output: 78

Approach:

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

1st term = 1 * ( 2(1) + 1 ) = 3

2nd term = 2 * ( 2(2) + 1 ) = 10

3rd term = 3 * ( 2(3) + 1 ) = 21

4th term = 4 * ( 2(4) + 1 ) = 36

.

.

Nth term = N * ( 2(N) + 1 )

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

TN =  N * ( 2(N) + 1 )

Illustration:

Input: N = 10
Output: 210
Explanation:
TN = N * ( 2(N) + 1 )
= 10 * ( 2(10) + 1 )
= 210

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` `nTh(``int` `n)` `{` `    ``return` `n * (2 * n + 1);` `}`   `// Driver code` `int` `main()` `{` `    ``int` `N = 10;` `    ``cout << nTh(N) << endl;` `    ``return` `0;` `}`

## C

 `// C program to implement` `// the above approach` `#include `   `// Function to return` `// Nth term of the series` `int` `nTh(``int` `n)` `{` `    ``return` `n * (2 * n + 1);` `}`   `// Driver code` `int` `main()` `{` `    ``// Value of N` `    ``int` `N = 10;` `    ``printf``(``"%d"``, nTh(N));` `    ``return` `0;` `}`

## Java

 `// Java program to implement` `// the above approach` `import` `java.io.*;`   `class` `GFG {` `    ``// Driver code` `    ``public` `static` `void` `main(String[] args)` `    ``{` `        ``int` `N = ``10``;` `        ``System.out.println(nTh(N));` `    ``}`   `    ``// Function to return` `    ``// Nth term of the series` `    ``public` `static` `int` `nTh(``int` `n)` `    ``{` `        ``return` `n * (``2` `* n + ``1``);` `    ``}` `}`

## Python

 `# Python program to implement` `# the above approach`   `# Function to return` `# Nth term of the series` `def` `nTh(n):` `    `  `    ``return` `n ``*` `(``2` `*` `n ``+` `1``)` `    `  `# Driver code`   `N ``=` `10` `print``(nTh(N))`   `# This code is contributed by Samim Hossain Mondal.`

## C#

 `using` `System;`   `public` `class` `GFG` `{`   `  ``// Function to return` `  ``// Nth term of the series` `  ``public` `static` `int` `nTh(``int` `n)` `  ``{` `    ``return` `n * (2 * n + 1);` `  ``}` `  ``static` `public` `void` `Main (){`   `    ``// Code` `    ``int` `N = 10;` `    ``Console.Write(nTh(N));` `  ``}` `}`   `// This code is contributed by Potta Lokesh`

## Javascript

 ``

Output

`210`

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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