Final answer:
To determine the number of seats in the eighth row of the theater, which follows an arithmetic sequence with a common difference of 5, we used the formula for the nth term of an arithmetic sequence to find that there are 47 seats in the eighth row.
Step-by-step explanation:
How to Find the Number of Seats in the Eighth Row
Let's address the given question step by step. The scenario presented is a classic example of an arithmetic sequence, where the number of seats increases by a fixed amount (which is 5 in this case) with each subsequent row. To find out how many seats are in the eighth row, we need to use the formula for finding the nth term of an arithmetic sequence:
an = a1 + (n - 1)d
where:
- an is the nth term we are looking to find – the number of seats in the eighth row.
- a1 is the first term – the number of seats in the first row, which is 12.
- n is the term number – in this case, 8 since we are looking for the eighth row.
- d is the common difference between the terms – the increment of seats from one row to the next, which is 5.
According to this formula, we calculate the number of seats in the eighth row:
a8 = 12 + (8 - 1) × 5
a8 = 12 + 7 × 5
a8 = 12 + 35
a8 = 47
Therefore, the eighth row has 47 seats.