ACT Math · Sequences and series

A theater has 20 seats in the first row. Each subsequent row has 4 more seats than the row before it. How many seats are in the 10th row?

A theater has 20 seats in the first row. Each subsequent row has 4 more seats than the row before it. How many seats are in the 10th row?

Answer and explanation

Answer: A: 56

The seat counts form an arithmetic sequence with first term 2020 and common difference 44. The nnth term is an=20+4(n−1)a_n=20+4(n-1), so the 1010th row has 20+4(9)=20+36=5620+4(9)=20+36=56 seats, choice A. Choice D (6060) uses n=10n=10 rather than n−1=9n-1=9 additional steps, which is the 1111th row. Choice B (4444) uses 66 steps. Choice C (4040) uses 55 steps. The first row is the starting term, so the number of added differences is one less than the row number.

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