The price of a certain item was $10 in 1990 and it has gone up by $2 per year since 1990. If this trend continues, in what year will the price be $100?
A large solid cube is assembled by gluing together identical unpainted small cubic blocks. All six faces of the large cube are then painted red. If exactly 27 of the small cubic blocks that make up the large cube have no paint on them, how many small cubic blocks make up the large cube?
You don't want to use the summation formula if you are going to use the arithmetic progression approach, you want to use the formula for the nth term:
With we find:
You see, we want the value of n - 1, not n, as year zero is 1990, not year 1.
if 27 cubes have no face painted then have the next bigger cube made be gluing small cubes on each face to complete the cube. Since the bigger cube is made of smaller cubes it should have 64 small cubes. Because 3 cube is 27 and 4 cube is 64. Now you can proceed further