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Find n-th term in the series 9, 33, 73,129 …
• Difficulty Level : Easy
• Last Updated : 16 Apr, 2021

Given a series 9, 33, 73, 129… Find the n-th term of the series.
Examples:

```Input : n = 4
Output : 129

Input : n = 5
Output : 201```

The given series has a pattern which is visible after subtracting it from itself after one shift

```S = 9 + 33 + 73 + 129 + … tn-1 + tn
S =     9 + 33 + 73 + … tn-2 + tn-1 + tn
———————————————
0 = 9 + (24 + 40 + 56 + ….) - tn

Since 24 + 40 + 56.. series in A.P with
common difference of 16, we get

tn = 9 + [((n-1)/2)*(2*24 + (n-1-1)d)]

On solving this we get

tn = 8n2 + 1```

Below is the implementation of the above approach:

## C++

 `// Program to find n-th element in the``// series 9, 33, 73, 128..``#include ``using` `namespace` `std;` `// Returns n-th  element of the series``int` `series(``int` `n)``{``    ``return` `(8 * n * n) + 1;``}` `// driver program to test the above function``int` `main()``{``    ``int` `n = 5;``    ``cout << series(n);``    ``return` `0;``}`

## Java

 `// Program to find n-th element in the``// series 9, 33, 73, 128..``import` `java.io.*;` `class` `GFG{``    ` `    ``// Returns n-th  element of the series``    ``static` `int` `series(``int` `n)``    ``{``        ``return` `(``8` `* n * n) + ``1``;``    ``}``    ` `    ``// driver program to test the above``    ``// function``    ``public` `static` `void` `main(String args[])``    ``{``        ``int` `n = ``5``;``        ``System.out.println(series(n));``    ``}``}` `/*This code is contributed by Nikita Tiwari.*/`

## Python3

 `# Python Program to find n-th element``# in the series 9, 33, 73, 128...` `# Returns n-th element of the series``def` `series(n):``    ``print` `(( ``8` `*` `n ``*``*` `2``) ``+` `1``)``    ` `# Driver Code``series(``5``)` `# This code is contributed by Abhishek Agrawal.`

## C#

 `// C# program to find n-th element in the``// series 9, 33, 73, 128..``using` `System;` `class` `GFG {` `    ``// Returns n-th element of the series``    ``static` `int` `series(``int` `n)``    ``{``        ``return` `(8 * n * n) + 1;``    ``}` `    ``// driver function``    ``public` `static` `void` `Main()``    ``{``        ``int` `n = 5;``        ``Console.WriteLine(series(n));``    ``}``}` `/*This code is contributed by vt_m.*/`

## PHP

 ``

## Javascript

 ``

Output:

`201`

Time complexity: O(1)
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