Difference between revisions of "1988 AHSME Problems/Problem 30"

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[[Category: Intermediate Algebra Problems]]
 
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Revision as of 08:29, 23 October 2014

Problem

Let $f(x) = 4x - x^{2}$. Give $x_{0}$, consider the sequence defined by $x_{n} = f(x_{n-1})$ for all $n \ge 1$. For how many real numbers $x_{0}$ will the sequence $x_{0}, x_{1}, x_{2}, \ldots$ take on only a finite number of different values?

$\textbf{(A)}\ \text{0}\qquad \textbf{(B)}\ \text{1 or 2}\qquad \textbf{(C)}\ \text{3, 4, 5 or 6}\qquad\\ \textbf{(D)}\ \text{more than 6 but finitely many}\qquad\\ \textbf{(E) }\infty$


Solution

See also

1988 AHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 29
Followed by
Last Question
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