SM cinema has 24 seats in the 1st row, and each of the succeeding rows has 2 more seats than the row before it. If there are 16 rows of seats, what is its seating capacity?
16th row has ... 24 + (2 * 15) = 54
average row length ... (24 + 54) / 2
capacity is ... number of rows * average row length
Well, let's start off with the first row, which has 24 seats. If each succeeding row has 2 more seats than the row before it, that means the second row would have 24 + 2 seats, and the third row would have 24 + 2 + 2 seats, and so on.
To find the total seating capacity, we need to calculate the number of seats in each row and sum them up.
Let's do the math together, shall we?
First row: 24 seats
Second row: 24 + 2 = 26 seats
Third row: 24 + 2 + 2 = 28 seats
...
Sixteenth row: 24 + (16 - 1) * 2 = 24 + 30 = 54 seats
Now, let's add up the number of seats in each row:
24 + 26 + 28 + ... + 54
To find the sum of an arithmetic series, we can use the formula: S = (n / 2)(2a + (n - 1)d), where S is the sum, n is the number of terms, a is the first term, and d is the common difference.
In this case, n = 16 (the number of rows), a = 24 (the first term), and d = 2 (the common difference).
S = (16 / 2)(2 * 24 + (16 - 1) * 2)
Simplifying it further: S = 8(48 + 15 * 2) = 8(48 + 30) = 8(78) = 624
Therefore, the seating capacity of SM cinema is a whopping 624 seats! Enjoy the show!
To find the seating capacity of SM cinema, we need to calculate the total number of seats in all the rows.
The first row has 24 seats.
Starting from the second row, each row has 2 more seats than the row before it.
So, the second row has 24 + 2 = 26 seats.
The third row has 26 + 2 = 28 seats.
By following this pattern, we can determine the number of seats in each of the 16 rows:
Row 4: 28 + 2 = 30 seats
Row 5: 30 + 2 = 32 seats
Row 6: 32 + 2 = 34 seats
Row 7: 34 + 2 = 36 seats
Row 8: 36 + 2 = 38 seats
Row 9: 38 + 2 = 40 seats
Row 10: 40 + 2 = 42 seats
Row 11: 42 + 2 = 44 seats
Row 12: 44 + 2 = 46 seats
Row 13: 46 + 2 = 48 seats
Row 14: 48 + 2 = 50 seats
Row 15: 50 + 2 = 52 seats
Row 16: 52 + 2 = 54 seats
To find the seating capacity, we sum up the number of seats in each row:
24 + 26 + 28 + 30 + 32 + 34 + 36 + 38 + 40 + 42 + 44 + 46 + 48 + 50 + 52 + 54 = 640
Therefore, the seating capacity of SM cinema is 640.
To find the seating capacity of SM cinema, we need to calculate the total number of seats in each row and then sum them up.
In the first row, there are 24 seats.
For the subsequent rows, each row has 2 more seats than the row before it. This means the second row has 24 + 2 = 26 seats, the third row has 26 + 2 = 28 seats, and so on.
We can create a sequence to represent the number of seats in each row. The first row has 24 seats and each subsequent row has 2 more seats than the previous row. This sequence can be represented as:
24, 26, 28, 30, ...
Using this arithmetic sequence, we can find the number of seats in the 16 rows by finding the 16th term of the sequence.
16th term = first term + (number of terms - 1) * common difference
By substituting the values into the formula, we get:
16th term = 24 + (16 - 1) * 2
= 24 + 15 * 2
= 24 + 30
= 54
Therefore, the 16th row has 54 seats.
To find the total seating capacity, we sum up the number of seats in each row:
Total seating capacity = sum of the seats in each row
= 24 + 26 + 28 + ... + 54
We have an arithmetic series with a first term of 24, common difference of 2, and 16 terms.
Sum of an arithmetic series = (number of terms / 2) * (2 * first term + (number of terms - 1) * common difference)
By substituting the values into the formula, we get:
Total seating capacity = (16 / 2) * (2 * 24 + (16 - 1) * 2)
= 8 * (48 + 15 * 2)
= 8 * (48 + 30)
= 8 * 78
= 624
Therefore, the seating capacity of SM cinema is 624.