Determine the seating capacity of an auditorium with 10 rows of seats if there are 10 seats in the first row, 16 seats in the second row, 22 seats in the third row, 28 seats in the forth row, and so on
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To determine the seating capacity of the auditorium, you need to find the pattern in the number of seats in each row. Here, the pattern seems to be that the number of seats in each row increases by 6 seats compared to the previous row.
Let's list the number of seats in each row:
- First row: 10 seats
- Second row: 10 + 6 = 16 seats
- Third row: 16 + 6 = 22 seats
- Fourth row: 22 + 6 = 28 seats
- Fifth row: 28 + 6 = 34 seats
- Sixth row: 34 + 6 = 40 seats
- Seventh row: 40 + 6 = 46 seats
- Eighth row: 46 + 6 = 52 seats
- Ninth row: 52 + 6 = 58 seats
- Tenth row: 58 + 6 = 64 seats
Now that we have the number of seats in each row, we can find the seating capacity by adding up all the seats in each row.
Seating capacity = 10 + 16 + 22 + 28 + 34 + 40 + 46 + 52 + 58 + 64
To simplify the calculation, we can use the formula for the sum of an arithmetic sequence. The sum of an arithmetic sequence is given by the formula:
Sum = (n/2) * (first term + last term)
Where n is the number of terms, the first term is the number of seats in the first row, and the last term is the number of seats in the last row.
In this case, the number of terms (n) is 10, the first term is 10, and the last term is 64.
Using the formula, we can calculate the seating capacity:
Sum = (10/2) * (10 + 64) = 5 * 74 = 370.
Therefore, the seating capacity of the auditorium with 10 rows of seats, following the given pattern, is 370.
looks like an arithemetic progression, is 10, then each row increases by 6
Isn't there a neat formula for that?