1988 AHSME Problems/Problem 30

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

1988 AHSME (Problems • Answer Key • Resources)
Preceded by Problem 29	Followed by Last Question
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
All AHSME Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.

Page

Toolbox

Search

1988 AHSME Problems/Problem 30

Problem

Solution

See also