# Find n-th term of series 3, 9, 21, 41, 71…

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
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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 (Σn2)+(Σn)+1, where

So, for calculating any n-th term of given series say f(n) we have:
f(n) = (Σn2)+(Σn)+1
= ( ((n*(n+1)*(2n+1))/6) + (n*(n+1)/2) + 1
= (n3+ 3n2 + 2n + 3 ) /3

## C++

 `// Program to calculate  ` `// nth term of a series ` `#include ` `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

 ` `

Output :

```241
911```

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