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Find n-th term of series 3, 9, 21, 41, 71…
• Last Updated : 07 Apr, 2021

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 (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

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## Javascript

 ``

Output :

```241
911```

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