Chapter 1.1, Problem 48E

In Exercises 47-52, use inductive reasoning to predict the next line in each sequence of computations. Then use a calculator or perform the arithmetic by hand to determine whether your conjecture is correct.

$\begin{array}{c}3+6=\frac{6\times 3}{2}\\ 3+6+9=\frac{9\times 4}{2}\\ 3+6+9+12=\frac{12\times 5}{2}\\ 3+6+9+12+15=\frac{15\times 6}{2}\end{array}$