# 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

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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 get t_{n = 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 <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;` `}` |

## 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

`<?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.` `?>` |

## Javascript

`<script>` `// 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 program to test the above function` `let n = 5;` `document.write(series(n));` `</script>` |

**Output: **

201

**Time complexity:** O(1)

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