Question

Length of one Total # of # of
side of pattern triangular white
(in cm) Shapes used triang-
to make pattern ular
shapes
used
2 4 3
3 9 6
4 16 10
? ? ?
6 ? ?
? ? ?
? ? ?
20 ? ?

Number of gray triangular shapes used 1, 3,6,? ? ? ? ?

Answer 1

observation #1:
what happens when you square the numbers in the first column?

observation #2
in the third column:
second # - first # = ??
third # - second # = ??

observation #3

visualize billiard balls racked up

sum of balls after 1 row = 1
sum of balls after 2 rows = 3
sum of balls after 3 rows = 6
....

Answer 2

Ok Reiny i get that i have to square the 1st row to come up with the 2nd row, but i still don't get how i come up with the 3rd row?

Answer 3

2 4 3
3 9 6
4 16 10
? ? ?
6 ? ?
? ? ?
? ? ?
20 ? ?
Third column
6-3 = 3
10-6 = 4
then
15-5 = 5
21-15 = 6
28-21 = 7

so
3
6
10
15
21
28
etc