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Find nth term of the series 5 2 13 41
• Last Updated : 20 Apr, 2021

Given a number N, the task is to find the nth term of the series

5, 2, 19, 13, 41, 31, 71, 57….

It is given that value of n can range between 1 and 10000.
Examples:

```Input: N = 4
Output:13

Input: N = 15
Output:272```

Approach: The problem looks very hard but approach is very simple. If the value of n is given as an odd number, the nth term will be ( ( n + 1 ) ^ 2 ) + n.
Otherwise, it will be ( ( n – 1 ) ^ 2 ) + n.

Implementation:

## C++

 `// C++ program to find nth term of``// the series 5 2 13 41``#include``using` `namespace` `std;` `// function to calculate nth term of the series``int` `nthTermOfTheSeries(``int` `n)``{``    ``// to store the nth term of series``    ``int` `nthTerm;` `    ``// if n is even number``    ``if` `(n % 2 == 0)``        ``nthTerm = ``pow``(n - 1, 2) + n;` `    ``// if n is odd number``    ``else``        ``nthTerm = ``pow``(n + 1, 2) + n;` `    ``// return nth term``    ``return` `nthTerm;``}` `// Driver code``int` `main()``{``    ``int` `n;` `    ``n = 8;``    ``cout << nthTermOfTheSeries(n) << endl;` `    ``n = 12;``    ``cout << nthTermOfTheSeries(n) << endl;` `    ``n = 102;``    ``cout << nthTermOfTheSeries(n) << endl;` `    ``n = 999;``    ``cout << nthTermOfTheSeries(n) << endl;` `    ``n = 9999;``    ``cout << nthTermOfTheSeries(n) << endl;` `    ``return` `0;``}` `// This code is contributed``// by Akanksha Rai`

## C

 `// C program to find nth term of``// the series 5 2 13 41``#include ``#include ` `// function to calculate nth term of the series``int` `nthTermOfTheSeries(``int` `n)``{``    ``// to store the nth term of series``    ``int` `nthTerm;` `    ``// if n is even number``    ``if` `(n % 2 == 0)``        ``nthTerm = ``pow``(n - 1, 2) + n;` `    ``// if n is odd number``    ``else``        ``nthTerm = ``pow``(n + 1, 2) + n;` `    ``// return nth term``    ``return` `nthTerm;``}` `// Driver code``int` `main()``{``    ``int` `n;` `    ``n = 8;` `    ``printf``(``"%d\n"``, nthTermOfTheSeries(n));` `    ``n = 12;``    ``printf``(``"%d\n"``, nthTermOfTheSeries(n));` `    ``n = 102;``    ``printf``(``"%d\n"``, nthTermOfTheSeries(n));` `    ``n = 999;``    ``printf``(``"%d\n"``, nthTermOfTheSeries(n));` `    ``n = 9999;``    ``printf``(``"%d\n"``, nthTermOfTheSeries(n));` `    ``return` `0;``}`

## Java

 `// Java program to find nth term of the series 5 2 13 41` `import` `java.lang.Math;``class` `GFG``{``// function to calculate nth term of the series``static` `long`  `nthTermOfTheSeries(``int` `n)``{``    ``// to store the nth term of series``    ``long` `nthTerm;` `    ``// if n is even number``    ``if` `(n % ``2` `== ``0``)``        ``nthTerm = (``long``)Math.pow(n - ``1``, ``2``) + n;` `    ``// if n is odd number``    ``else``        ``nthTerm = (``long``)Math.pow(n + ``1``, ``2``) + n;` `    ``// return nth term``    ``return` `nthTerm;``}` `// Driver code``public` `static` `void` `main(String[] args)``{``    ``int` `n;` `    ``n = ``8``;` `    ``System.out.println( nthTermOfTheSeries(n));` `    ``n = ``12``;``    ``System.out.println( nthTermOfTheSeries(n));` `    ``n = ``102``;``    ``System.out.println( nthTermOfTheSeries(n));` `    ``n = ``999``;``    ``System.out.println( nthTermOfTheSeries(n));``    ` `    ``n = ``9999``;``    ``System.out.println( nthTermOfTheSeries(n));``//This code is contributed by  29AjayKumar` `}``}`

## Python3

 `# Python3 program to find nth term``# of the series 5 2 13 41``from` `math ``import` `pow` `# function to calculate nth term``# of the series``def` `nthTermOfTheSeries(n):``    ` `    ``# to store the nth term of series``    ``# if n is even number``    ``if` `(n ``%` `2` `=``=` `0``):``        ``nthTerm ``=` `pow``(n ``-` `1``, ``2``) ``+` `n` `    ``# if n is odd number``    ``else``:``        ``nthTerm ``=` `pow``(n ``+` `1``, ``2``) ``+` `n` `    ``# return nth term``    ``return` `nthTerm` `# Driver code``if` `__name__ ``=``=` `'__main__'``:``    ` `    ``n ``=` `8``    ``print``(``int``(nthTermOfTheSeries(n)))` `    ``n ``=` `12``    ``print``(``int``(nthTermOfTheSeries(n)))` `    ``n ``=` `102``    ``print``(``int``(nthTermOfTheSeries(n)))` `    ``n ``=` `999``    ``print``(``int``(nthTermOfTheSeries(n)))` `    ``n ``=` `9999``    ``print``(``int``(nthTermOfTheSeries(n)))` `# This code is contributed by``# Shashank_Sharma`

## C#

 `// C# program to find nth term``// of the series 5 2 13 41``using` `System;` `class` `GFG``{``    ``// function to calculate``    ``// nth term of the series``    ``static` `long` `nthTermOfTheSeries(``int` `n)``    ``{``        ``// to store the nth term of series``        ``long` `nthTerm;``    ` `        ``// if n is even number``        ``if` `(n % 2 == 0)``            ``nthTerm = (``long``)Math.Pow(n - 1, 2) + n;``    ` `        ``// if n is odd number``        ``else``            ``nthTerm = (``long``)Math.Pow(n + 1, 2) + n;``    ` `        ``// return nth term``        ``return` `nthTerm;``    ``}``    ` `    ``// Driver code``    ``public` `static` `void` `Main()``    ``{``        ``int` `n;``    ` `        ``n = 8;``        ``Console.WriteLine(nthTermOfTheSeries(n));``    ` `        ``n = 12;``        ``Console.WriteLine( nthTermOfTheSeries(n));``    ` `        ``n = 102;``        ``Console.WriteLine( nthTermOfTheSeries(n));``    ` `        ``n = 999;``        ``Console.WriteLine( nthTermOfTheSeries(n));``        ` `        ``n = 9999;``        ``Console.WriteLine( nthTermOfTheSeries(n));``    ``}``}` `// This code is contributed by Ryuga`

## PHP

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## Javascript

 ``
Output:
```57
133
10303
1000999
100009999```

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