Final answer:
Alexander has a recursive sequence for grading papers where the initial amount is 96 papers, and the number decreases by 11 every hour (an = an-1 - 11), with n representing the number of hours he has graded.
Step-by-step explanation:
Alexander starts with 96 papers to grade. If he grades at a rate of 11 papers per hour, the remaining number of papers after n hours can be represented by a recursive sequence. The initial condition is a0 = 96, which indicates the number of papers before he starts grading. The recursive formula will subtract 11 from the previous term, so it looks like an = an-1 - 11, for n > 0.
To write the recursive sequence for the given situation, it can be presented as follows:
- For n = 0 (before starting):
- a
- 0
- = 96
- For n > 0 (after n hours of work):
- a
- n
- = a
- n-1
- - 11
- , with the condition that
- a
- n
- >= 0