  The solvable Farb growth of a group quantifies how well-approximated the
group is by its finite solvable quotients. In this note we present a new
characterization of polycyclic groups which are virtually nilpotent. That is,
we show that a group has solvable Farb growth which is at most polynomial in
$\log(n)$ if and only if the group is polycyclic and virtually nilpotent. We
also give new results concerning approximating oriented surface groups by
nilpotent quotients. As a consequence of this, we prove that a natural number
$C$ exists so that any nontrivial element of the $Ck$th term of the lower
central series of a finitely generated oriented surface group must have word
length at least $k$. Here $C$ depends only on the choice of generating set.
Finally, we give some results giving new lower bounds for the solvable Farb
growth of some metabelian groups (including the Lamplighter groups).
