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Another Sequence Problem

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January 11, 2009

Problem Statement

The sequence a1 a_1, a2 a_2, a3 a_3, … \dots satisfies a_1 \equal{} 19, a_9 \equal{} 99, and, for all n≥3 n \ge 3, an a_n is the arithmetic mean of the first n \minus{} 1 terms. Find a2 a_2. <spanclass=′latex−bold′>(A)</span> 29<spanclass=′latex−bold′>(B)</span> 59<spanclass=′latex−bold′>(C)</span> 79<spanclass=′latex−bold′>(D)</span> 99<spanclass=′latex−bold′>(E)</span> 179 <span class='latex-bold'>(A)</span>\ 29\qquad <span class='latex-bold'>(B)</span>\ 59\qquad <span class='latex-bold'>(C)</span>\ 79\qquad <span class='latex-bold'>(D)</span>\ 99\qquad <span class='latex-bold'>(E)</span>\ 179
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