Question

A chain email tells people to forward the email to 10 friends in order to have good luck. Assuming that everyone in the chain actually follows the directions, create a sequence to show how many people will get the email after 5 rounds of forwarding.(2 points) 10, 100, , , . . .

Answer 1

In this chain email scenario, each person forwards the email to 10 friends. Hence, the number of people receiving the email after each round can be calculated as follows:

- **Round 0 (initial sender):** 1 person
- **Round 1 (first forwards to 10):** 10 new people (total: 1 + 10 = 11)
- **Round 2 (each of those 10 forwards to 10 more):** 10 * 10 = 100 new people (total: 1 + 10 + 100 = 111)
- **Round 3 (each of those 100 forwards to 10 more):** 100 * 10 = 1000 new people (total: 1 + 10 + 100 + 1000 = 1111)
- **Round 4 (each of those 1000 forwards to 10 more):** 1000 * 10 = 10000 new people (total: 1 + 10 + 100 + 1000 + 10000 = 11111)
- **Round 5 (each of those 10000 forwards to 10 more):** 10000 * 10 = 100000 new people (total: 1 + 10 + 100 + 1000 + 10000 + 100000 = 111111)

So the sequence representing the number of new people receiving the email after each round (excluding the initial sender) would be:

- After round 1: 10
- After round 2: 100
- After round 3: 1000
- After round 4: 10000
- After round 5: 100000

Thus, the full sequence of the number of new people reached after each round (excluding the original sender) is:

10, 100, 1000, 10000, 100000.