Question

a41 - arithmetic sequences score: 18/19 answered: 18/19 question 19 sequences and series a theater has increasing rows of seats. there are 32 seats in the first row, 37 seats in the second row, 42 seats in the third row and so on. determine which row the number of seats reaches 247 rows question help: message instructor

Explanation:

Step1: Identify the arithmetic sequence

The first term \( a_1 = 32 \), common difference \( d = 37 - 32 = 5 \) (or \( 42 - 37 = 5 \)). The formula for the \( n \)-th term of an arithmetic sequence is \( a_n = a_1 + (n - 1)d \).

Step2: Substitute values into the formula

We know \( a_n = 247 \), \( a_1 = 32 \), \( d = 5 \). So:
\[
247 = 32 + (n - 1) \times 5
\]

Step3: Solve for \( n \)

First, subtract 32 from both sides:
\[
247 - 32 = (n - 1) \times 5
\]
\[
215 = (n - 1) \times 5
\]
Then divide both sides by 5:
\[
n - 1 = \frac{215}{5} = 43
\]
Finally, add 1 to both sides:
\[
n = 43 + 1 = 44
\]

Answer:

44