The first row of an auditorium has 34 seats and each next row has 7 more seats. How many seats are there in 21 rows?

Correct answer: 2184

This is an arithmetic-progression word problem because the number of seats increases by the same amount, 7, from one row to the next. The first term is a = 34, the common difference is d = 7, and the number of rows is n = 21. Since the question asks for the total, use S_n = n/2[2a + (n − 1)d]. Substitution gives S_21 = 21/2[2(34) + 20(7)] = 21/2[68 + 140] = 21/2 × 208 = 21 × 104 = 2184. Therefore, option C is correct. The distractors can result from using the nth-term formula instead of the sum formula, omitting a row, or making an arithmetic error. The constant increase confirms that AP methods are appropriate.