SOLUTION: Let x-2,2√ 3, x-3 be the first 3 terms of a geometric sequence. Find the value of x (the quadratic equation can be solved by factoring).
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Question 986739: Let x-2,2√ 3, x-3 be the first 3 terms of a geometric sequence. Find the value of x (the quadratic equation can be solved by factoring).
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
.
Since , and are the first 3 terms of a geometric sequence, you have a proportion
=
(saying that the ratio of the second term to the first one is equal to the ratio of the third term to the second one).
From the proportion,
(x-2)*(x-3) = = 4*3 = 12.
Hence,
= ,
= ,
(x+1)*(x-6) = 0.
The roots are -1 and 6.
Answer. x = -1 or x = 6.
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