SOLUTION: Find the value of x so that x, x + 2, and x + 3 are terms of a geometric sequence. Thank you in advance!

Question 765571: Find the value of x so that x, x + 2, and x + 3 are terms of a geometric sequence.
Thank you in advance!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
These terms are in a geometric sequence if you divide any term by the previous term and you get the same r value

(x + 2)/x = r

(x+3)/(x+2) = r

Equate the two and solve for x

(x + 2)/x = (x+3)/(x+2)

(x + 2)(x+2) = x(x+3)

x^2 + 4x + 4 = x^2 + 3x

x^2 + 4x + 4 - x^2 = x^2 + 3x - x^2

4x + 4 = 3x

4x = 3x - 4

4x - 3x = - 4

x = - 4

So the answer is x = -4

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