# Find n-th term in the series 9, 33, 73,129 …

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
```

## Recommended: Please solve it on “PRACTICE” first, before moving on to the solution.

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

 ` `

Output:

```201
```

Time complexity: O(1)

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Improved By : jit_t

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