How many triangles when there are five levels? 10 levels?

n |
Triangluar Numbers | Up | Down | Total Trianlges |

1 | 1 | 1 | 0 | 1 |

2 | 3 | 4 | 1 | 5 |

3 | 6 | 10 | 3 | 13 |

4 | 10 | 20 | 7 | 27 |

5 | 15 | 35 | 13 | 48 |

6 | 21 | 56 | 22 | 78 |

7 | 28 | 84 | 34 | 118 |

8 | 36 | 120 | 50 | 170 |

9 | 45 | 165 | 70 | 235 |

10 | 55 | 220 | 95 | 315 |

I was able to come up with the above table after making a sketch pad drawing such as the one below and then making a table on my notebook paper. I took the hint about number of triangles that point up and down and was able to see a pattern.

My next question was could I come up with a general formula for n levels?

Let t(n)= the number of triangles for a given n level

the summation of T(n), where T(n) is

and n begins at 1 and continues until the nth level.

The number of triangles that point down can be found by

dn= T(n -1)-dn-1

Where

Therefore the total number of triangles can be found by

Total = T(n-1)- dn-1 + S T(n)

**Click here to
return to my Emat 6690 page**