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 numbersis useful.

Hint:Count the number of triangles of

each sizein two parts: those pointing up and those pointing down.

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