To determine the number of people in the park at noon, we can use the formula for calculating the sum of an arithmetic sequence.
S_n=n(a_1+a_n)/2
From a previous exercise we know that the arithmetic sequence that describes the number of people has a first term of 300. We are also given that the number of people entering the amusement park each 15 minutes increased steadily by 250.
We also know that the number of people who entered the parade at noon was 4050. Let's now find how many 15-minutes intervals there are between 8:15 and noon. Remember that we evaluate the difference between the hours.
12:00 - 8:15 = 3:45
Recall that there are four 15-minutes intervals in each hour.
3 * 4 + 3 = 15
Therefore, there were fifteen 15-minutes intervals after 8:15 before the parade started. When we consider 300 people as the first term of the sequence, it gives us a total of 16 terms in the sequence. We can now substitute a_1 = 300, a_n= 4050, and n= 16 into the formula to calculate the sum.
