Question 1064175: Suppose x, y, z is a geometric sequence with common ratio r and x≠ y. If x, 2y, 3z is an arithmetic sequence, then what is r^2?
Answer by ikleyn(52800)   (Show Source):
You can put this solution on YOUR website! .
I will only give you a HINT, leaving the solution to you.
HINT 1. Since x, y ans z form Geom.progression, y = rx and z = r^2*x. (1)
HINT 2. Since x, 2y and 3z form Arithm.progression, 2y-x = 3z - 2y. (2)
HINT 3. Having this, substitute (1) to (2). You will get an equation
2(r*x) -x = 3(r^2*x) - 2*(r*x).
Cancel x in both sides and solve for "r".
Happy solving !!
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