Black Eyed Peas’ 2011 Live Concert is to take place in a circular park. Due to the shape of the area, seats are set up so that the innermost row has 64 seats and each successive row has 17 more seats than the row before it. The park’s open area can accommodate 17 rows of seats in this pattern. What is the maximum number of tickets that can be distributed if everyone who has a ticket is guaranteed a seat?
so you are adding
64 + 81 + 98 + ... for 17 terms
a = 64
d = 17
n = 17
use the formula
Sum(17) = (17/2)[128 + 16(17)]
= 3400
To find the maximum number of tickets that can be distributed, we need to determine the total number of seats in all the rows.
Given that the innermost row has 64 seats and each successive row has 17 more seats than the previous row, we can calculate the number of seats in each row.
The first row has 64 seats.
The second row has 64 + 17 = 81 seats.
The third row has 81 + 17 = 98 seats.
And so on, until the seventeenth row.
To find the number of seats in the seventeenth row, we can calculate it using the formula:
Number of seats in the nth row = Number of seats in the previous row + 17
Thus, the seventeenth row has 64 + (16 * 17) = 312 seats.
Now, we need to find the total number of seats in these 17 rows. We can use the formula for the sum of an arithmetic sequence to do this.
Sum of an arithmetic sequence = (first term + last term) * number of terms / 2
To find the sum of the 17 rows, we can substitute the values into the formula:
Sum = (64 + 312) * 17 / 2 = 376 * 17 / 2 = 3208
Therefore, the maximum number of tickets that can be distributed is 3208.