Geometric Series Word Problem

Question

A large school board established a phone tree to contact all of its employees in case of emergencies or inclement weather. Each of the three superintendents calls three employees who each in turn calls three other employees and so on. How many rounds of phone calls are needed to notify all 9840 employees?

Answer 1

The common ratio is 3.

 

9840 = 3(1 - 3ⁿ) / (1 - 3)

9840 = 3(1 - 3ⁿ) / -2

9840 = 3(1 - 3ⁿ)

-19680 = 3(1 - 3ⁿ)

-6560 = 1 - 3ⁿ

-6561 = -3ⁿ

6561 = 3ⁿ

8 = n