To B or Not To B

The first four terms of a pattern are shown below:

ABBA

AABBBAA

AAABBBBAAA

AAAABBBBBAAAA

Suppose that this pattern continues.

1. Find an expression for the number of B's in the nth term of the pattern.

2. Find an expression for the ratio of B's to total letters in the nth term.

3. Use your expression to determine which term has exactly 34% B's.

Extra: Can you find a term in the pattern that has exactly one-third B's and two-thirds A's?

Why or why not?