# 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

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

S = 9 + 33 + 73 + 129 + … t_{n-1}+ t_{n}S = 9 + 33 + 73 + … t_{n-2}+ t_{n-1}+ t_{n}——————————————— 0 = 9 + (24 + 40 + 56 + ….) - t_{n}Since 24 + 40 + 56.. series in A.P with common difference of 16, we get t_{n}= 9 + [((n-1)/2)*(2*24 + (n-1-1)d)] On solving this we gett_{n}= 8n^{2}+ 1

Below is the implementation of the above approach:

## C++

`// Program to find n-th element in the ` `// series 9, 33, 73, 128.. ` `#include <bits/stdc++.h> ` `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; ` `} ` |

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## 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.*/` |

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## 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. ` |

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## 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.*/` |

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## PHP

`<?php ` `// PHP Program to find n-th element ` `// in the series 9, 33, 73, 128.. ` ` ` `// Returns n-th element ` `// of the series ` `function` `series(` `$n` `) ` `{ ` ` ` `return` `(8 * ` `$n` `* ` `$n` `) + 1; ` `} ` ` ` `// Driver Code ` `$n` `= 5; ` `echo` `(series(` `$n` `)); ` ` ` `// This code is contributed by Ajit. ` `?> ` |

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Output:

201

**Time complexity:** O(1)

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