Difference between revisions of "1989 AHSME Problems/Problem 10"

(Created page with "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 va...")
 
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<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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Revision as of 13:48, 5 July 2013

Consider the sequence defined recursively by $u_1=a$ (any positive number), and $u_{n+1}=-1/(u_n+1)$, $n=1,2,3,...$ For which of the following values of $n$ must $u_n=a$?

$\mathrm{(A) \ 14 } \qquad \mathrm{(B) \ 15 } \qquad \mathrm{(C) \ 16 } \qquad \mathrm{(D) \ 17 } \qquad \mathrm{(E) \ 18 }$ The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. AMC logo.png