Given a mathematical series as 3, 9, 21, 41, 71… For a given integer n, you have to find the nth number of this series. **Examples :**

Input : n = 4 Output : 41 Input : n = 2 Output : 9

Our first task for solving this problem is to crack the series. If you will gave a closer look on the series, for a general n-th term the value will be **(Σn ^{2})+(Σn)+1**, where

**(Σn**: is sum of squares of first n-natural numbers.^{2})**(Σn)**: is sum of first n-natural numbers.- 1 is a simple constant value.

So, for calculating any n-th term of given series say f(n) we have: **f(n) = (Σn ^{2})+(Σn)+1**

= ( ((n*(n+1)*(2n+1))/6) + (n*(n+1)/2) + 1

= (n

^{3}+ 3n

^{2}+ 2n + 3 ) /3

## C++

`// Program to calculate` `// nth term of a series` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// func for calualtion` `int` `seriesFunc(` `int` `n)` `{` ` ` `// for summation of square` ` ` `// of first n-natural nos.` ` ` `int` `sumSquare = (n * (n + 1)` ` ` `* (2 * n + 1)) / 6;` ` ` `// summation of first n natural nos.` ` ` `int` `sumNatural = (n * (n + 1) / 2);` ` ` `// return result` ` ` `return` `(sumSquare + sumNatural + 1);` `}` `// Driver Code` `int` `main()` `{` ` ` `int` `n = 8; ` ` ` `cout << seriesFunc(n) << endl;` ` ` ` ` `n = 13;` ` ` `cout << seriesFunc(13);` ` ` ` ` `return` `0;` `}` |

## Java

`// Java Program to calculate` `// nth term of a series` `import` `java.io.*;` `class` `GFG` `{` ` ` `// func for calualtion` ` ` `static` `int` `seriesFunc(` `int` `n)` ` ` `{` ` ` `// for summation of square` ` ` `// of first n-natural nos.` ` ` `int` `sumSquare = (n * (n + ` `1` `)` ` ` `* (` `2` `* n + ` `1` `)) / ` `6` `;` ` ` ` ` `// summation of first n natural nos.` ` ` `int` `sumNatural = (n * (n + ` `1` `) / ` `2` `);` ` ` ` ` `// return result` ` ` `return` `(sumSquare + sumNatural + ` `1` `);` ` ` `}` ` ` ` ` `// Driver Code` ` ` `public` `static` `void` `main(String args[])` ` ` `{` ` ` `int` `n = ` `8` `;` ` ` `System.out.println(seriesFunc(n));` ` ` ` ` `n = ` `13` `;` ` ` `System.out.println(seriesFunc(` `13` `));` ` ` `}` `}` `// This code is contributed by Nikita Tiwari.` |

## Python3

`# Program to calculate` `# nth term of a series` `# func for calualtion` `def` `seriesFunc(n):` ` ` `# for summation of square` ` ` `# of first n-natural nos.` ` ` `sumSquare ` `=` `(n ` `*` `(n ` `+` `1` `) ` `*` ` ` `(` `2` `*` `n ` `+` `1` `)) ` `/` `6` ` ` `# summation of first n` ` ` `# natural nos.` ` ` `sumNatural ` `=` `(n ` `*` `(n ` `+` `1` `) ` `/` `2` `)` ` ` `# return result` ` ` `return` `(sumSquare ` `+` `sumNatural ` `+` `1` `)` `# Driver Code` `n ` `=` `8` `print` `(` `int` `(seriesFunc(n)))` `n ` `=` `13` `print` `(` `int` `(seriesFunc(n)))` `# This is code is contributed by Shreyanshi Arun.` |

## C#

`// C# program to calculate` `// nth term of a series` `using` `System;` `class` `GFG` `{` ` ` `// Function for calualtion` ` ` `static` `int` `seriesFunc(` `int` `n)` ` ` `{` ` ` `// For summation of square` ` ` `// of first n-natural nos.` ` ` `int` `sumSquare = (n * (n + 1)` ` ` `* (2 * n + 1)) / 6;` ` ` ` ` `// summation of first n natural nos.` ` ` `int` `sumNatural = (n * (n + 1) / 2);` ` ` ` ` `// return result` ` ` `return` `(sumSquare + sumNatural + 1);` ` ` `}` ` ` ` ` `// Driver Code` ` ` `public` `static` `void` `Main()` ` ` `{` ` ` `int` `n = 8;` ` ` `Console.WriteLine(seriesFunc(n));` ` ` ` ` `n = 13;` ` ` `Console.WriteLine(seriesFunc(13));` ` ` `}` `}` `// This code is contributed by vt_m.` |

## PHP

`<?php` `// Program to calculate` `// nth term of a series` `// func for calualtion` `function` `seriesFunc(` `$n` `)` `{` ` ` `// for summation of square` ` ` `// of first n-natural nos.` ` ` `$sumSquare` `= (` `$n` `* (` `$n` `+ 1)` ` ` `* (2 * ` `$n` `+ 1)) / 6;` ` ` `// summation of first n natural nos.` ` ` `$sumNatural` `= (` `$n` `* (` `$n` `+ 1) / 2);` ` ` `// return result` ` ` `return` `(` `$sumSquare` `+ ` `$sumNatural` `+ 1);` `}` `// Driver Code` `$n` `= 8;` `echo` `(seriesFunc(` `$n` `) . ` `"\n"` `);` ` ` `$n` `= 13;` `echo` `(seriesFunc(` `$n` `) . ` `"\n"` `);` `// This code is contributed by Ajit.` `?>` |

## Javascript

`<script>` `// JavaScript Program to calculate` `// nth term of a series` ` ` `// func for calualtion` ` ` `function` `seriesFunc(n)` ` ` `{` ` ` `// for summation of square` ` ` `// of first n-natural nos.` ` ` `let sumSquare = (n * (n + 1)` ` ` `* (2 * n + 1)) / 6;` ` ` ` ` `// summation of first n natural nos.` ` ` `let sumNatural = (n * (n + 1) / 2);` ` ` ` ` `// return result` ` ` `return` `(sumSquare + sumNatural + 1);` ` ` `}` ` ` `// Driver code` ` ` `let n = 8;` ` ` `document.write(seriesFunc(n) + ` `"<br/>"` `);` ` ` ` ` `n = 13;` ` ` `document.write(seriesFunc(13));` `</script>` |

**Output :**

241 911

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