2013 - 27 & 28

Some people like these questions. I don't care for them and I rarely attempt them on the test.

 

Difficulty: I guess it's a medium, but I have no real sense 'cause I didn't try it !

Difficulty: Medium, if they have done conics; hard, if not.

Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest 2013

answer 27, answer 28. Published 4/30.