The first term is the second term divided by the common ratio r.



The third term is the second term multiplied by the common ratio r.

Clear the fraction by multiplying through by r





Divide through by 2



Arrange in descending order



Factor:



Use zero-factor property:

3r+1=0;   r+3=0
  3r=-1;    r=-3
   r=

So there will be two solutions to this problem.

Using r=, the sequence is









-18,6,-2,

Fourth term = 

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Using r = -3, the sequence is









-2, 6, -18, 54

Fourth term = 54.

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Edwin