Difference between revisions of "1989 AHSME Problems/Problem 10"
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| + | == Problem == | ||
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Consider the sequence defined recursively by <math>u_1=a</math> (any positive number), and <math>u_{n+1}=-1/(u_n+1)</math>, <math>n=1,2,3,...</math> For which of the following values of <math>n</math> must <math>u_n=a</math>? | Consider the sequence defined recursively by <math>u_1=a</math> (any positive number), and <math>u_{n+1}=-1/(u_n+1)</math>, <math>n=1,2,3,...</math> For which of the following values of <math>n</math> must <math>u_n=a</math>? | ||
<math> \mathrm{(A) \ 14 } \qquad \mathrm{(B) \ 15 } \qquad \mathrm{(C) \ 16 } \qquad \mathrm{(D) \ 17 } \qquad \mathrm{(E) \ 18 } </math> | <math> \mathrm{(A) \ 14 } \qquad \mathrm{(B) \ 15 } \qquad \mathrm{(C) \ 16 } \qquad \mathrm{(D) \ 17 } \qquad \mathrm{(E) \ 18 } </math> | ||
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| + | == Solution == | ||
| + | == See also == | ||
| + | {{AHSME box|year=1989|num-b=9|num-a=11}} | ||
| + | |||
| + | [[Category: Introductory Algebra Problems]] | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 07:49, 22 October 2014
Problem
Consider the sequence defined recursively by 
(any positive number), and 
, 
For which of the following values of 
must 
?
Solution
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. 
