MathDB
quadratic sequence

Source: 0

April 23, 2009
quadraticsarithmetic sequence

Problem Statement

a_{1} \equal{}1, a_{n\plus{}1} \equal{}\frac{a_{n} }{\sqrt{1\plus{}4a_{n}^{2} } } for n1 n\ge 1. What is the least k k such that a_{k} <10^{\minus{}2} ?
<spanclass=latexbold>(A)</span> 2501<spanclass=latexbold>(B)</span> 251<spanclass=latexbold>(C)</span> 2499<spanclass=latexbold>(D)</span> 249<spanclass=latexbold>(E)</span> None<span class='latex-bold'>(A)</span>\ 2501 \qquad<span class='latex-bold'>(B)</span>\ 251 \qquad<span class='latex-bold'>(C)</span>\ 2499 \qquad<span class='latex-bold'>(D)</span>\ 249 \qquad<span class='latex-bold'>(E)</span>\ \text{None}