Hints and solutions to Look for a pattern #9
If you add 6 rows to the bottom of the picture below, how many small
triangles
will you have altogether?
- Well, you could draw the picture and try and count all the
triangles,
but it might be better to look for a pattern.
- We're only counting little triangles here, so let's start by
counting how many are in each row.
- Looks like there is 1 triangle in the top row, then 3 in the second
row,
5 in the third, and so forth.
- In the picture so far, there are 1 + 3 + 5 + 7 triangles. This is
the sum
of the first four odd numbers and remember back to the very first POD,
this
is 42=16.
- So if we add six more rows, we'll have the sum of the first 10 odd
numbers,
so the total number of small triangles will be 102 =
100.