Question

a41 - arithmetic sequences
score: 17/19 answered: 17/19
question 18
sequences
determine the how many seats in a theater with 36 rows of seats, on the 36th row if there are 28 seats in
the first row, 32 seats in the second row, 36 seats in the third row and so on.
seats
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Explanation:

Step1: Identify the arithmetic sequence

The number of seats per row forms an arithmetic sequence where the first term \(a_1 = 28\), the common difference \(d = 32 - 28 = 4\) (since \(32 - 28 = 4\) and \(36 - 32 = 4\)).

Step2: Use the formula for the nth term of an arithmetic sequence

The formula for the nth term of an arithmetic sequence is \(a_n = a_1 + (n - 1)d\). We need to find the 36th term, so \(n = 36\), \(a_1 = 28\), \(d = 4\).
Substitute the values into the formula: \(a_{36} = 28 + (36 - 1) \times 4\)

Step3: Calculate the value

First, calculate \(36 - 1 = 35\). Then, \(35 \times 4 = 140\). Finally, \(28 + 140 = 168\).

Answer:

168