1989 AHSME Problems/Problem 10
Problem
Consider the sequence defined recursively by (any positive number), and , For which of the following values of must ?
Solution
Repeatedly applying the function, and simplifying, we get and then again. So must appear at every third term after . The only option given of the form is .
See also
1989 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 9 |
Followed by Problem 11 | |
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.