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

m (See also)
(Problem)
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<math>\textbf{(A)}\ \text{0}\qquad
 
<math>\textbf{(A)}\ \text{0}\qquad
 
\textbf{(B)}\ \text{1 or 2}\qquad
 
\textbf{(B)}\ \text{1 or 2}\qquad
\textbf{(C)}\ \text{3, 4, 5 or 6}\qquad\\
+
\textbf{(C)}\ \text{3, 4, 5 or 6}\qquad
\textbf{(D)}\ \text{more than 6 but finitely many}\qquad\\
+
\textbf{(D)}\ \text{more than 6 but finitely many}\qquad
\textbf{(E) }\infty</math>  
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\textbf{(E) }\infty</math>
 
 
  
 
==Solution==
 
==Solution==

Revision as of 04:56, 14 April 2016

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
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