Chapter 1.2, Problem 18ES

Pieces vs. Cuts One straight cut across a pizza produces $2$ pieces. Two cuts can produce a maximum of $4$ pieces. Three cuts can produce a maximum of $7$ pieces. Four cuts can produce a minimum of $11$ pieces.

a. Use a difference table to predict the maximum number of pieces that can be produced with seven cuts.

b. How are the pizza-slicing numbers related to the triangular numbers, which are defined by $Triangula{r}_n=\frac{n\left(n+1\right)}{2}$?