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**A school phone tree has 1 person responsible for contacting 3 people. If there are 1500 students in the school, how many levels will there be on the phone tree (assuming 1 person is at the top of the tree)?**

__My Solution:__This question forms a geometric series:

A(first term)=1

R(common ratio)=3

1+3+9+27......

Let n= # of levels to the phone tree

When will the sum of the series equal 1500?

Sn=A(1-R^n)/(1-R)

1500=1(1-(3^n))/(1-(3))

-3000=1-(3)^n

-3001=-(3^n)

3001=(3^n)

Log(3001)=nLog(3)

Log(3001)/Log(3)

~7.29

An 8th level would have to be added to the tree; however, the level would not be complete. 8 levels to the tree.

Is this the correct solution to this question? Can you identify where and if I have gone wrong?

Thanks! Appreciate the help :)