Mock AIME 6 2006-2007 Problems/Problem 8
Problem
A sequence of positive reals defined by , , and for all integers . Given that and , find .
Solution
And the sequence repeats every 6 steps.
Therefore,
Since, and , then , and
From , we get , thus
and from , we get .
Therefore, which gives
Then, which gives which gives
Finally,
~Tomas Diaz. orders@tomasdiaz.com
Alternate solutions are always welcome. If you have a different, elegant solution to this problem, please add it to this page.