A theatre has (1740) seats in (20) rows. If each next row has (6) more seats, how many seats were in the first row?

Correct answer: (30)

The direct answer is B: 30 seats. Let the first row have a seats. There are 20 rows and each next row has 6 more seats, so the last row has a+19(6). The sum of an AP is S_n=n/2[2a+(n-1)d]. Substituting S_20=1740 and d=6 gives 1740=20/2[2a+19(6)]=10(2a+114). Thus 174=2a+114, so 2a=60 and a=30. Option B is correct. Option A, 28, would give total 1700; option C, 32, would give 1780; option D, 34, would give 1820. The common mistake is to divide the total by 20 and call that the first row; 87 is the average, not the first term. Since the rows increase, the first row must be below the average.