I'm stuck on this problem

Sam decides to start a rumor. Sam tells the rumor to her three friends. Each of Sam's three friends then tells the rumor to three friends who have not heard the rumor. This continues for five total cycles. Sam telling her three friends was the first cycle. How many people, not including Sam, will have heard the rumor when the fifth cycle is complete?

I tried 243, but it's wrong...

NJColonial6 Sep 12, 2022

#1**0 **

number of people who have heard the rumor after cycle 1 = 3

number of people who have heard the rumor after cycle 2 = 3 + (3 + 3 + 3)

number of people who have heard the rumor after cycle 2 = 3 + 3 * 3

number of people who have heard the rumor after cycle 2 = 3 + 3^{2}

number of people who have heard the rumor after cycle 3 = 3 + 3^{2} + 3^{2 }* 3

number of people who have heard the rumor after cycle 3 = 3 + 3^{2} + 3^{3}

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number of people who have heard the rumor after cycle 5 = 3 + 3^{2} + 3^{3} + 3^{4} + 3^{5} = 363

hectictar Sep 13, 2022