An auditorium has (2520) seats in (24) rows. If each next row has (5) more seats, how many seats were in the first row?

Correct answer: (47)

The correct answer is option B, 47 seats. The rows form an arithmetic progression because every row increases by the same number, 5. Here the number of rows is 24, the total is 2520, the common difference is 5, and the first term is a. Use \(S_n=\frac{n}{2}[2a+(n-1)d]\). Thus \(2520=\frac{24}{2}[2a+23(5)]\), so \(2520=12(2a+115)\). Dividing by 12 gives 210=2a+115, hence 2a=95 and a=47. Option A, 46, would give a total of 2508, not 2520. Option B, 47, gives the required total and is correct. Option C, 48, would make the total 2532. Option D, 49, would make it 2556. Remember: in an AP, total equals number of terms multiplied by the average of the first and last terms; always substitute the answer back to check.