Which one set of letters when sequentially placed at the gaps in the given letter series shall complete it ?

aab _ aa _ bbb _ aaa _ bbba

We check the options as follows:

Option 1) aaba/ aabbbb/ baaaabbb/ a. There is no clear pattern here. 

Option 2) aabb/ aaabbb/ aaaabbbb/ a. A clear pattern repeats itself. 

Option 3) aaba/ aaabbb/ aaaabbbb/ a. There is no clear pattern here.

Option 4) aaba/ aabbbb/ aaaabbbb/ a. There is no clear pattern here.

Therefore, there is a clear sequence followed in option 2. 

Hence, the correct answer is "Option 2".