Exercise 1 Page 400

Let's analyze the successive layers of the pyramid in the exercise. A sequence $a_n$ represents the number of cubes in $n^{\text{th}}$ layer. We are asked to find a rule for $a_n.$ Notice that in Layer $n$ we have $n$ $\text{rows}$ and $(n+1)$ $\text{columns}.$ Therefore, in the $n^{\text{th}}$ layer we have $n\cdot (n+1)$ cubes.