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?

sup

step-by-step explanation: