Mary splits an equilateral triangle into smaller triangles
and color-codes them, as shown in the figure below. The first time, she makes 3
white triangles and 1 black triangle. The second time, she makes 6 white triangles
and 3 black triangles. The third time, she makes 10 white triangles and 6 black
triangles. She continues this process.
How many black triangles does she make the tenth time?
How many black triangles does she make the twentieth time?