Real sequences $a_n$ and $b_n$ such that $\sum a_nb_n$ converges

Question

Is there no correct answer to this question?

For (a) and (c), I can take $a_n=0$ for all n, so $b_n$ can be unbounded. For (d), $a_n=0,1,0,2,0,3,...$ and $b_n=1,0,2,0,3,0,...$ shows both sequences can be unbounded.

So, is there no correct option or am I mistaken somewhere?