In a certain business meeting, the boss sits in the front row, which has only 1 seat. There are 30 rows in total. If each row after the front row has 3 more seats than the row before it, which expression gives the total number of seats in the last row?

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A great way to keep track of the pattern is with a simple table:

$$ \begin{array}{|c|c|} \hline \text{row number} & \text{number of seats} \\ \hline 1 & 1 \\ \hline 2 & 1+3 \\ \hline 3 & 1+3+3 \\ \hline ... & ... \\ \hline 1+29 & 1+29(3) \\ \hline \end{array} $$

In the 30^th row, we needed to add three 29 times to the initial 1^st seat.

\(1+29(3)\) is equivalent to \(\boxed{1+3(30-1)}\).

You might recognize the pattern as an arithmetic sequence with initial value \(a_1=1\) and difference \(d=3\).

$$ 1, 4, 7, 10, 13 ... $$ $$ a_n=a_1+d(n-1) $$ $$ a_{30}=1+3(30-1) $$ $$ a_{30}=\boxed{1+3(30-1)} $$