Write a rule for each pattern. then use your rule to find the next two terms in the pattern. the numbers are: 1, 3, 6, 10, 15, 21, 28, 36

This is the Triangular Number Sequence:

This sequence comes from a pattern of dots that form a triangle:

By adding another row of dots and counting all the dots we can 
find the next number of the sequence.

We can make a "Rule" so we can calculate any triangular number.

First, rearrange the dots (and give each pattern a number n), like this:

Then double the number of dots, and form them into a rectangle:

And we get (remembering we doubled the dots):

Rule: xn = n(n+1)/2

Example: the 5th Triangular Number is

x5 = 5(5+1)/2 = 15

Example: the 60th is

x60 = 60(60+1)/2 = 1830

Wasn't it much easier to use the formula than to add up all those dots?

glide reflection.

its mainly because the pattern will be infinite and will never end. it will look like a gilder or like a filpbook when set to motion.