We are making a sequence of triangles out of diamonds. The first three steps are complete. In each step a line of diamonds is added to the bottom. In the bottom line the two outside diamonds, one on each side are white. All the other diamonds in the triangle are black. How many black diamond will the figure have in step 6?
If I understand this right, the total number of diamonds after n steps is just
Sn = 1+2+3+...+n = n(n+1)/2
Finding the number of white diamonds should now be easy, and thus the number of blacks.