Question

it takes 6 cubes to build a staircase with 3 steps. how many cubes will be needed for 11 steps?

Answer 1

1 step -- 1 cube
2 steps - 3 cubes
3 steps - 6 cubes
4 steps - 10 cubes
.....
n steps - n(n+1)/2 cubes

so 11 steps --11(12)/2 = 66 cubes

these are called the triangular numbers
think of it as the sum of billiard balls when they are racked up
1st row -- one ball
2 rows --- 3 balls
etc.