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 $d=3$.

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