Question

Suppose that a chain letter is started by someone in the first week of the year. Each recipient of the chain letter mails copies on to five other people in the next week. After six weeks, how much money in postage (40c/ a letter) has been spent on these chain letters?

Answer 1

Explanation:

First person sends 5 in the first week.

In the second week, each recipient sends 5 letters each. The total number sent in the second week is 5 × 5 = 25

In the third week, each recipient sends 5 letters each. The total number sent in the second week is 5 × 25 = 125

In the fourth week, each recipient sends 5 letters each. The total number sent in the second week is 5 × 125 = 625

In the fifth week, each recipient sends 5 letters each. The total number sent in the second week is 5 × 625 = 3125

In the sixth week, each recipient sends 5 letters each. The total number sent in the second week is 5 × 3125 = 15625

Total number of letters sent in 6 weeks is

15625 + 3125 + 625 + 125 + 25 + 5 = 19530 letters

Total cost is

0.4 × 19530 = $7812