Problems(2)
A license plate in a certain state consists of 4 digits, not necessarily distinct, and 2 letters, also not necessarily distinct. These six characters may appear in any order, except that the two letters must appear next to each other. How many distinct license plates are possible?
<spanclass=′latex−bold′>(A)</span>104⋅262<spanclass=′latex−bold′>(B)</span>103⋅263<spanclass=′latex−bold′>(C)</span>5⋅104⋅262<spanclass=′latex−bold′>(D)</span>102⋅264<spanclass=′latex−bold′>(E)</span>5⋅103⋅263 AMC
Let a1,a2,... 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?<spanclass=′latex−bold′>(A)</span>21<spanclass=′latex−bold′>(B)</span>32<spanclass=′latex−bold′>(C)</span>23<spanclass=′latex−bold′>(D)</span>2<spanclass=′latex−bold′>(E)</span>3 AMC