Ans: $21$
Note that the number of seats in a row form an arithmetic sequence. Note also that the first term is $12$ and the common difference is $3$.
Note that the number of seats in a row form an arithmetic sequence. Note also that the first term is $12$ and the common difference is $3$.
Let $n$ be the number of rows in the theatre.
$\begin{array}{rcl}
\dfrac{n}{2}[2(12)+(n-1)(3)] & \le & 930 \\
n^2+7n-620 & \le & 0 \\
\end{array}$
$\therefore -28.6446\le n \le 21.6446$.
Therefore, the greatest number of rows in the theatre is $21$.
