Final answer:
To represent the total cost of admission for the number of visits in a season, an arithmetic sequence can be created with a common difference of $45. The cost of admission for the first visit is $45, and the sequence can be extended to five terms. To determine when a season pass becomes the better deal, compare the total cost of admission with the cost of a season pass. A person would have to visit the park at least 3 times for a season pass to be the better deal.
Step-by-step explanation:
a. To represent the total cost of admission for the number of visits in a season, we can create an arithmetic sequence. The common difference will be the cost of admission each time a person visits the park, which is $45. The first term can be the cost of admission for the first visit, which is also $45. So, the arithmetic sequence will be:
- Total: $45
- Total: $90
- Total: $135
- Total: $180
- Total: $225
b. To find out how many times a person has to visit the park for a season pass to be the better deal, we need to compare the total cost of admission for the number of visits with the cost of a season pass. In this case, the season pass costs $112 per person, so we need to find the number of visits that would equal or exceed the cost of a season pass. From the arithmetic sequence we created in part a, we can see that a person would have to visit the park at least 3 times for the total cost of admission to equal or exceed the cost of a season pass. Therefore, a person would have to visit the park at least 3 times for a season pass to be the better deal.