Question

Determine the seating capacity of an auditorium with 25 rows of seats if there are 20 seats in the first row, 24 in the second row, 28 in the third row, and so on.

Answer 1

To determine the seating capacity of the auditorium, use an arithmetic series to find the number of seats in each row and then sum them up.

Step-by-step explanation:

To determine the seating capacity of the auditorium, we need to find the number of seats in each row and then sum them up. The number of seats in each row follows a pattern of increasing by 4 seats with each row. Starting with 20 seats in the first row, the number of seats in each subsequent row can be found using the formula: 20 + 4(n-1), where n is the row number.

Using this formula, we can find the number of seats in each row:

1. Row 1: 20 seats
2. Row 2: 20 + 4(2-1) = 24 seats
3. Row 3: 20 + 4(3-1) = 28 seats
4. ...
5. Row 25: 20 + 4(25-1) = 116 seats

To find the seating capacity, we simply need to sum up the number of seats in each row:

Total seating capacity = 20 + 24 + 28 + ... + 116. This is an arithmetic series with a common difference of 4. We can use the formula for the sum of an arithmetic series to calculate this:

Total seating capacity = (25/2)(20 + 116) = 25(68) = 1700 seats.

Answer 2

The seats are increasing at a rate of four per row. If you were to write this in an equation, it would be y=4X+20, with 4 as the rate of change, 20 as the original amount of seats, and Y as the total number of seats for X rows. Plug in 25 for X and you'll get an answer of 120 seats.