Count the total number of triangles of any size.
Extend the sequence.Hints/Solution:
Did you get 1, 5, 13, 27 so far?
How many triangles when there are five levels of small triangles? 10 levels?
How do you verify your sequence?Is there a general formula for n levels?
Proof?
Comments:
Recognition of the sequence of triangular numbers is useful.
Hint:
Count the number of triangles of each size in two parts: those pointing up and those pointing down.