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

Answer 1

Assume each person forwards to 10 new people who haven't seen it. Then the number of new recipients in round n is

a_n = 10^n.

So the sequence for rounds 1–5 is:
10, 100, 1,000, 10,000, 100,000.

The total number of people who have gotten the email after 5 rounds is the sum
S5 = 10 + 100 + 1,000 + 10,000 + 100,000 = 111,110.

(If you also count the original sender, add 1 → 111,111.)