# Find nth term of the series 5 2 13 41

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

 ` `

Output:

```57
133
10303
1000999
100009999
```

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