SOLUTION: Find all the possible values of x such that this sequence is geometric: x,12,9x

Question 898312: Find all the possible values of x such that this sequence is geometric: x,12,9x
Answer by DrBeeee(684) (Show Source): You can put this solution on YOUR website!
In a geometric sequence each term is a constant, say c, times the previous term.
For the given sequence
(1) x, 12 , 9x we get
(2) 12 = cx or
(3) c = 12/x
Then we have for the third term
(4) 9x = (12/x)*12 or
(5) 9x^2 = 12^2 or
(6) x^2 = (12^2)/(3^2) or
(7) x = 12/3 or
(8) x = 4
Let's check this. Using (3) we get
(9) c = 12/4 or
(10) c = 3
The sequnce should be
(11) 4, 3*4, 3*3*4 or
(12) 4, 12, 36 or
(13) 4, 12, 9*4
I believe that x = 4 is the only possible solution.
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