A bank account has a balance of $120 on January 1. Describe a situation in which the account balance for each month (February 1, March 1, . . .) forms these types of sequences. Write the first three terms of each sequence.

1. an arithmetic sequence
2. a geometric sequence

On May 12, a fast-growing species of algae is accidentally introduced into a pond in a park. The area of the pond that the algae covers doubles each day. If not controlled, the algae will cover the entire surface of the pond, depriving the fish in the pond of oxygen. At the rate it is growing, this will happen on May 24.

1. On which day is the pond halfway covered?
2. On May 18, Clare visits the park. A park caretaker mentions to her that the pond will be completely covered in less than a week. Clare looks at how much of the pond is currently covered and thinks that the caretaker must be mistaken. Why might she find the caretaker’s claim hard to believe?
3. What fraction of the area of the pond was covered by the algae initially, on May 12? Explain or show your reasoning.