The 300 people who were lined up outside the amusement park had all entered by 8:15, and by 8:30, $550$ more had entered. The number who entered each 15 minutes increased steadily by $250$ after that, and all were planning to stay for the parade.

1. How many people entered between 11:45 and 12:00 noon, just in time for the parade?

   Answer (a):

   $4050$

2. Represent the problem as a series and write a formula for the n^th term.

   Hint (b):

   Write the summation representing the total number of people who entered the amusement park to see the parade between 8:15 and 12:00.
   Write the formula for the sequence representing the number of people who entered the park during the n^th quarter-hour