In a movie theater, theater A has 30 seats in the first row. Each next row has 4 more seats in it than the previous row has.

1) How many seats are in the 4th row?

2) Is there a row with exactly 60 seats in it?

3) Theater B has 40 seats in the first row and each row has 4 more seats than the previous row. If both Theater A and Theater B has 25 rows, how many seats does Theater B have in it than Theater A?

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Please check the first two Related Questions below.

1. 46 seats...... 30+4+4+4+4

2. No the 8th row has 62 seats and the 7th row has 58
(30+4+4+4+4+4+4+4+4)
3.THeater B has 145 seats....
(40+25 4's)
hope that helped

1. 46 because a1=30 a2=34 a3=38 a4=42

2.No the 8th row is is 58 and the 9th row is 62.
3. 40+(25x4) = 140

1) To find the number of seats in the 4th row of Theater A, we need to determine the pattern. The first row has 30 seats, and each subsequent row has 4 more seats than the previous row.

Let's calculate:

1st row = 30 seats
2nd row = 30 + 4 = 34 seats
3rd row = 34 + 4 = 38 seats
4th row = 38 + 4 = 42 seats

Therefore, the 4th row of Theater A has 42 seats.

2) To check if there is a row with exactly 60 seats, we can continue the pattern above until we reach a row with 60 seats. However, it's more efficient to use an algebraic equation:

Let x be the number of rows after the first row.
Number of seats in the (x+1)th row = 30 + 4x.

We want to find the value of x that makes the number of seats in the (x+1)th row equal to 60. So we set up the equation:

30 + 4x = 60

Solving this equation, we get:

4x = 60 - 30
4x = 30
x = 30 / 4
x = 7.5

Since the number of rows cannot be a decimal, there is no row with exactly 60 seats in Theater A.

3) To find the difference in the number of seats between Theater A and Theater B, we need to calculate the total number of seats each theater has.

Theater A has 25 rows, and the number of seats in each row follows the pattern described earlier (30 + 4x).

Calculating the total number of seats in Theater A:

Total seats in Theater A = (30 + 34 + 38 + ... + [30 + 4 * 24])

To find this sum, we can use the arithmetic series formula:

Sum = (n/2) * (first term + last term)

In this case, n (number of terms) = 25, first term = 30, last term = 30 + 4 * (25 - 1).

Plugging these values into the formula, we get:

Sum = (25/2) * (30 + 30 + 4 * (25 - 1))

Calculating this sum gives us the total number of seats in Theater A.

Similarly, we can calculate the total number of seats in Theater B using the same formula but with different values (first term = 40, last term = 40 + 4 * (25 - 1)).

Once we have the total number of seats in both theaters, we can find the difference between them.