# Sequences

### Example 1

A giant cookie sits on a plate. Cookie Monster eats half the cookie with one bite. With another bite he eats half of the remaining cookie.

Cookie Monster keeps taking bites, eating half the remaining cookie with each bite.

(a) After 5 bites, what fraction of the cookie has Cookie Monster eaten?

(b) How many bites does it take before less than one one-thousandth of the cookie remains?

### Example 2

A dress is listed at $150. At the end of each week the price is reduced by 10%.

(a) What is the price of the dress after 8 weeks?

(b) After how many weeks will the dress be less than $50?

(hint: If 10% of the price is taken off, then 90% of the price remains.)

### Example 3

A dress is listed at $75. At the end of each week the price is reduced by $2.

(a) What is the price of the dress after 8 weeks?

(b) After how many weeks will the dress be less than $50?

### Example 4

During her first week of biking, Jenny bikes 3km per day. Each week, she bikes 3km farther per day than she did the previous week.

(a) How many weeks does it take Jenny to get up to 15km per day?

(b) How far does Jenny bike on her 31st day?

### Example 5

A particular drug decays in the system so that 1 day after taking a dose, 30% of the drug remains in the bloodstream. Paco takes one pill.

(a) What percent of the drug remains in Paco's bloodstream 5 days after taking one dose?

(b) How many days before less than 1% of the drug remains in Paco's bloodstream?