An auditorium with 52 rows is laid out where 6 seats comprise the first row, 9 seats comprise the second row, 12 seats comprise the third row. the number of seats increases by 3 per row. what is the seating capacity of the auditorium? 4,368 4,160 4,290 1,508

The number of seats per row generate an arithmetic sequence. Let denote the number of seats in the -th row. We're told that the number of seats increases by 3 per row, so we can describe the number of seats in a given row recursively by



The total number of seats is given by the summation



Because is arithmetic, we can easily find an explicit rule for the sequence.







So the number of seats in the -th row is exactly



This means the total number of seats is



You should be familiar with the remaining sums. We end up with