The problem in the image states:

In a movie theater, there are 15 rows of seats. The first row has 16 seats. In each subsequent row, 2 additional seats are added at both ends of the row. How many seats are there in the last row?

Solution:

This is an arithmetic sequence, where:

• The first term $a_1 = 16$ (the number of seats in the first row),
• The common difference $d = 2$, because 2 seats are added in each subsequent row.

The formula for the $n$-th term of an arithmetic sequence is:

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

Where:

• $a_n$ is the number of seats in the $n$-th row,
• $a_1 = 16$ (the number of seats in the first row),
• $d = 2$ (the difference in seats between rows),
• $n = 15$ (the last row).

Substituting the values:

$a_{15} = 16 + (15 - 1) \cdot 2$ $a_{15} = 16 + 14 \cdot 2$ $a_{15} = 16 + 28 = 44$

The number of seats in the 15th row is 44.

However, based on the choices in the image, they might refer to the total number of seats, or the description could be interpreted differently. If you're asking about total seats or another aspect, feel free to clarify.

Would you like further details on the reasoning, or do you have any additional questions?

Here are some related questions:

1. How do arithmetic sequences relate to geometric ones?
2. How can we find the sum of seats for all 15 rows?
3. Can we calculate the total increase in seats from row 1 to row 15?
4. What happens if the difference between rows changes over time?
5. Can the same method be applied to different seat configurations?

Tip: Always check the exact wording of the problem to confirm whether it asks for a final count or a total sum.