This problem describes an arithmetic sequence where the first row has 9 seats, and each successive row has 11 more seats than the previous row.

In an arithmetic sequence, the $n$-th term $a_n$ is given by the formula:

$a_n = a_1 + (n - 1) \cdot d$

where:

• $a_1$ is the first term (9 seats),
• $d$ is the common difference between terms (11 seats per row),
• $n$ represents the row number.

Applying the values: $a_n = 9 + (n - 1) \cdot 11$

Simplifying this does not alter the form of the answer since each option has been given in this form. This matches the first option:

$a_n = 9 + 11(n - 1)$

Correct Answer:

$a_n = 9 + 11(n - 1)$

Would you like further details on this?

Here are 5 related questions:

1. What is an arithmetic sequence, and how does it differ from a geometric sequence?
2. How would the formula change if each successive row had a different pattern of increase, such as doubling seats?
3. Can we calculate the number of seats in a specific row, say the 10th row, using the given formula?
4. How can we derive the total number of seats up to a certain row in this sequence?
5. If the first row had a different starting number of seats, how would it affect the sequence formula?

Tip: In arithmetic sequences, remember the difference between $(n - 1)$ and $(n + 1)$ in the formula, as it controls whether the sequence "starts from" the first term.