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.

Question

10, 100, _____, _____, _____

Answer 1

In this chain email scenario, each person forwards the email to 10 friends. Here's how the number of people who receive the email grows round by round:

1. Round 0 (initial sender): 1 person sends the email.
2. Round 1: The initial sender forwards to 10 friends, so 10 people receive the email.
3. Round 2: Each of those 10 people forwards the email to 10 friends, resulting in \(10 \times 10 = 100\) new recipients.
4. Round 3: Each of those 100 people forwards to 10 friends, resulting in \(100 \times 10 = 1,000\) new recipients.
5. Round 4: Each of those 1,000 people forwards the email to 10 friends, resulting in \(1,000 \times 10 = 10,000\) new recipients.
6. Round 5: Each of those 10,000 people forwards the email to 10 friends, resulting in \(10,000 \times 10 = 100,000\) new recipients.

So the complete sequence after 5 rounds of forwarding is:

• Round 0: 1 person (initial sender)
• Round 1: 10 people
• Round 2: 100 people
• Round 3: 1,000 people
• Round 4: 10,000 people
• Round 5: 100,000 people

Therefore, the sequence is: 10, 100, 1,000, 10,000, 100,000.