Question

The Greek theater shown at the right has 30 seats in the first row of the center section. Each row behind

the first row gains two additional seats. How many seats are in the 5th row in the center section?
B 38
C 40
TA​

Answer 1

To find the number of seats in the 5th row of the Greek theater, we use the arithmetic progression formula, with the first term as 30 and the common difference as 2. Calculating the 5th term gives us 38 seats in the 5th row.

Step-by-step explanation:

The question asks how many seats are in the 5th row of the center section of a Greek theater, given that the first row has 30 seats and each subsequent row adds two seats more than the previous row. To calculate this, we need to use arithmetic progression, where the first term (a1) is 30 (the number of seats in the first row) and the common difference (d) is 2 (the number of additional seats in each row).

To find the number of seats in the 5th row, we need to find the 5th term of the arithmetic sequence. The general formula for the nth term of an arithmetic sequence is given by:

an = a1 + (n - 1)d

Substituting the values we have,

a5 = 30 + (5 - 1) × 2

a5 = 30 + (4)(2)

a5 = 30 + 8 = 38

So, there are 38 seats in the 5th row of the center section of the Greek theater.