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Turkey NMO 2008 1st Round - P15 (Algebra)

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August 25, 2012

Problem Statement

Let the sequence (an)(a_n) be defined as a1=13a_1=\frac 13 and an+1=an1+13an2a_{n+1}=\frac{a_n}{\sqrt{1+13a_n^2}} for every n≥1n\geq 1. If aka_k is the largest term of the sequence satisfying ak<150a_k < \frac 1{50}, what is kk?
<spanclass=′latex−bold′>(A)</span> 194<spanclass=′latex−bold′>(B)</span> 193<spanclass=′latex−bold′>(C)</span> 192<spanclass=′latex−bold′>(D)</span> 191<spanclass=′latex−bold′>(E)</span> None of the above <span class='latex-bold'>(A)</span>\ 194 \qquad<span class='latex-bold'>(B)</span>\ 193 \qquad<span class='latex-bold'>(C)</span>\ 192 \qquad<span class='latex-bold'>(D)</span>\ 191 \qquad<span class='latex-bold'>(E)</span>\ \text{None of the above}
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