1999 AHSME Problems/Problem 13

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Problem

Define a sequence of real numbers $a_1$ , $a_2$ , $a_3$ , $\dots$ by $a_1 = 1$ and $a_{n\plus{}1}^3 = 99a_n^3$ (Error compiling LaTeX. Unknown error_msg) for all $n \geq 1$ . Then $a_{100}$ equals

$\textbf{(A)}\ 33^{33} \qquad \textbf{(B)}\ 33^{99} \qquad \textbf{(C)}\ 99^{33} \qquad \textbf{(D)}\ 99^{99} \qquad \textbf{(E)}\ \text{none of these}$

Solution

1999 AHSME (Problems • Answer Key • Resources)
Preceded by Problem 12	Followed by Problem 14
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30
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1999 AHSME Problems/Problem 13

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