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1989 AHSME Problems/Problem 10

Revision as of 06:08, 19 February 2012 by Ckorr2003 (talk | contribs) (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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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 $u_n=a$?

$\mathrm{(A) \ 14 } \qquad \mathrm{(B) \ 15 } \qquad \mathrm{(C) \ 16 } \qquad \mathrm{(D) \ 17 } \qquad \mathrm{(E) \ 18 }$

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