Triangle Numbers | ||
---|---|---|

Rows | Triangle(Rows) | Formula |

1 | 1 | base case |

2 | 3 | 2 + Triangle(1) |

3 | 6 | 3 + Triangle(2) |

4 | 10 | 4 + Triangle(3) |

5 | 15 | 5 + Triangle(4) |

6 | 21 | 6 + Triangle(5) |

7 | 28 | 7 + Triangle(6) |

The table shows values of the `Triangle()`

function.
For example, `Triangle(4) = 10`

.
But it stops at seven. What is `Triangle(12)`

?

We have already figured out that the following is true:

total number of pins in N rows = number of pins in row N + total number of pins in N-1 rows = N + total number of pins in N-1 rows

This can be written as a formula:

Triangle( N ) = N + Triangle( N - 1 )

So the number of pins in a