The seats in the rows of an auditorium are arranged so that they form an arithmetic progression down the rows.
(i) The 12th row contains 51 seats and the total number of seats in the first 12 rows is 414. Determine the number of seats in the first row and the common difference between successive rows.
(ii) Using the values found in (i), calculate the total number of seats in the first 30 rows.
(iii) Which row contains exactly 75 seats?