MathDB
Real Number Sequence

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January 11, 2009
ratiogeometric sequence

Problem Statement

Define a sequence of real numbers a1 a_1, a2 a_2, a3 a_3, … \dots by a1=1 a_1 = 1 and an+13=99an3 a_{n + 1}^3 = 99a_n^3 for all n≥1 n \ge 1. Then a100 a_{100} equals
<spanclass=′latex−bold′>(A)</span> 3333<spanclass=′latex−bold′>(B)</span> 3399<spanclass=′latex−bold′>(C)</span> 9933<spanclass=′latex−bold′>(D)</span> 9999<spanclass=′latex−bold′>(E)</span> none of these <span class='latex-bold'>(A)</span>\ 33^{33} \qquad <span class='latex-bold'>(B)</span>\ 33^{99} \qquad <span class='latex-bold'>(C)</span>\ 99^{33} \qquad <span class='latex-bold'>(D)</span>\ 99^{99} \qquad <span class='latex-bold'>(E)</span>\ \text{none of these}
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