The $300$ people who are lined up outside an amusement park all enter by 8:15 a.m. By 8:30, $550$ more people enter. After 8:30, every $15$ minutes the number of people who enter increases steadily by $250$. All of the people are planning to stay for the parade at noon.

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

   Answer (a):

   $4050$

2. Represent the problem as a sequence 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.