Answer
$230$ units
Work Step by Step
We have a sequence \(\{a_n\}\) that increases by 2 units each day. Let \(a_0 = 170\) be the productivity on day $0$. Then each day we add $2$ units:
\[
a_{n} = a_{n-1} + 2, \quad n \ge 1.
\]
A direct closed-form formula for such an arithmetic sequence is
\[
a_n = a_0 + 2n.
\]
Therefore, on day $30$, the worker must produce
\[
a_{30} = 170 + 2 \times 30 = 170 + 60 = 230
\]
units to qualify for the bonus.
