Question

you are creating a window display at a toy store using wooden blocks. the display involves stacking blocks in triangular forms. you begin to display with 1 block, which is your first "triangle," and then stack three blocks, two on the bottom and one on the top, to get the next triangle. you create the next three triangles by stacking 6 blocks, then 10 blocks, and then 15 blocks. how many blocks will you need for the ninth triangle?

Answer 1

Your numbers are called "triangular" numbers and are found in Pascal's triangle.
see:
http://milan.milanovic.org/math/english/triangular/triangular.html