# Number of cards needed build a House of Cards of a given level N

Given a number **N**, the task is to find the number of cards needed to make a House of Cards of N levels.

**Examples:**

Input:N = 3Output:15

From the above image, it is clear that for the House of Cards for 3 levels 15 cards are neededInput:N = 2Output:7

**Approach:**

- If we observe carefully, then a series will be formed as shown below in which i-th item denotes the number of triangular cards needed to make a pyramid of
**i**levels:

2, 7, 15, 26, 40, 57, 77, 100, 126, 155………and so on.

- The above series is a method of difference series where differences are in AP as 5, 8, 11, 14……. and so on.

- Therefore nth term of the series will be:

nth term = 2 + {5 + 8 + 11 +14 +.....(n-1) terms} = 2 + (n-1)*(2*5+(n-1-1)*3)/2 = 2 + (n-1)*(10+(n-2)*3)/2 = 2 + (n-1)*(10+3n-6)/2 = 2 + (n-1)*(3n+4)/2 = n*(3*n+1)/2;

- Therefore the number of cards needed for building a House of Cards of N levels will be:

Below is the implementation of the above approach:

## CPP

`// C++ implementation of the above approach` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to find number of cards needed` `int` `noOfCards(` `int` `n)` `{` ` ` `return` `n * (3 * n + 1) / 2;` `}` `// Driver Code` `int` `main()` `{` ` ` `int` `n = 3;` ` ` `cout << noOfCards(n) << ` `", "` `;` ` ` `return` `0;` `}` |

## Java

`// Java implementation of the above approach` `import` `java.lang.*;` `class` `GFG` `{` ` ` `// Function to find number of cards needed` ` ` `public` `static` `int` `noOfCards(` `int` `n)` ` ` `{` ` ` `return` `n * (` `3` `* n + ` `1` `) / ` `2` `;` ` ` `}` ` ` ` ` `// Driver Code` ` ` `public` `static` `void` `main(String args[])` ` ` `{` ` ` `int` `n = ` `3` `;` ` ` `System.out.print(noOfCards(n));` ` ` `}` `}` `// This code is contributed by shubhamsingh10` |

## Python3

`# Python3 implementation of the above approach` `# Function to find number of cards needed` `def` `noOfCards(n):` ` ` `return` `n ` `*` `(` `3` `*` `n ` `+` `1` `) ` `/` `/` `2` `# Driver Code` `n ` `=` `3` `print` `(noOfCards(n))` `# This code is contributed by mohit kumar 29` |

## C#

`// C# implementation of the above approach` `using` `System;` `class` `GFG` `{` ` ` `// Function to find number of cards needed` ` ` `public` `static` `int` `noOfCards(` `int` `n)` ` ` `{` ` ` `return` `n * (3 * n + 1) / 2;` ` ` `}` ` ` ` ` `// Driver Code` ` ` `public` `static` `void` `Main(String []args)` ` ` `{` ` ` `int` `n = 3;` ` ` `Console.Write(noOfCards(n));` ` ` `}` `}` `// This code is contributed by 29AjayKumar` |

## Javascript

`<script>` `// Javascript implementation of the above approach` `// Function to find number of cards needed` `function` `noOfCards(n)` `{` ` ` `return` `parseInt(n * (3 * n + 1) / 2);` `}` `// Driver Code` `var` `n = 3;` `document.write(noOfCards(n));` `</script>` |

**Output:**

15

**Time Complexity:** O(1)

**Auxiliary Space: **O(1)