2002 #13 and 29

Patterns!

Difficulty: Easier than it looks. Getting students to begin seems to be the key.

Difficulty: Patterns, again.

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

answer 13 and answer 29.