MathDB
Sequences

Source: AMC 10 2006B, Problem 18

February 17, 2006
AMC

Problem Statement

Let a1,a2,... a_1, a_2, ... be a sequence for which a_1 \equal{} 2\,\hspace{.2in}a_2 \equal{} 3\, \hspace{.2in}\text{and}\hspace{.2in}a_n \equal{} \frac {a_{n \minus{} 1}}{a_{n \minus{} 2}} \text{ for each positive integer } n \ge 3.What is a2006 a_{2006}?
<spanclass=latexbold>(A)</span>12<spanclass=latexbold>(B)</span>23<spanclass=latexbold>(C)</span>32<spanclass=latexbold>(D)</span>2<spanclass=latexbold>(E)</span>3<span class='latex-bold'>(A) </span> \frac 12 \qquad <span class='latex-bold'>(B) </span> \frac 23 \qquad <span class='latex-bold'>(C) </span> \frac 32 \qquad <span class='latex-bold'>(D) </span> 2 \qquad <span class='latex-bold'>(E) </span> 3