Question 18Let $a_1,$ $a_2,$ $\ldots$ be a sequence for which $a_1=2,$ $a_2=3,$ and $a_n=\dfrac{a_{n-1}}{a_{n-2}}$ for each positive integer $n\ge 3.$ What is $a_{2006}?$$\dfrac{1}{2}$$\dfrac{2}{3}$$\dfrac{3}{2}$$2$$3$