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Which of the following sequences describe the number of seats in the theater, where n represents the row number?

A. f(n) = 18(4)n
B. 18, 22, 26, ..., 74, 78
C. f(n) = 18 + (n-1) ⋅ 4, n ≥ 1
D. f(1) = 18, f(n) = f(n - 1) + 4, n ≥ 2
E. f(1) = 18, f(n) = f(n-1), n ≥ 2

User Neongrau
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1 Answer

3 votes

Final answer:

Options B, C, and D all represent plausible sequences for the number of seats in a theater, increasing by 4 seats each row, starting with 18 seats.

Step-by-step explanation:

The question asks which sequence describes the number of seats in a theater, given that n represents the row number. To determine the correct formula, we should consider how the number of seats increases with each row.

Let's analyze the options:

• Option A: f(n) = 18(4)n. This represents an exponential increase in seats, which is unlikely for a typical theater seating arrangement.

• Option B: 18, 22, 26, ..., 74, 78. This is a finite sequence with a clear pattern of increasing by 4 each time, which seems plausible.

• Option C: f(n) = 18 + (n-1) · 4, n ≥ 1. This is a recursive definition where each row has 4 more seats than the previous, starting with 18 in the first row.

• Option D: f(1) = 18, f(n) = f(n - 1) + 4, n ≥ 2. This is another way to define a sequence that increases by 4 with each term, starting from 18.

• Option E: f(1) = 18, f(n) = f(n-1), n ≥ 2. This indicates the number of seats would be the same in every row, which is not a pattern of increase.

From our analysis, Options B, C, and D describe a consistent pattern of increasing seats in each subsequent row by 4 and starting with 18 seats in the first row. Option A represents an exponential increase which isn't typical for theaters, and Option E suggests no change in the number of seats, which is also improbable. Therefore, either Option B, C, or D correctly represents the number of seats in the theater rows depending on how the question is interpreted, whether as a sequence list, a functional equation, or a recursive definition.

User David Moye
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