SOLUTION: if (x,y,12) is decreasing geometric sequence and (x,y,9) is arthemetic sequence then..evaluate the value of x,y and find Gn

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Question 1044383: if (x,y,12) is decreasing geometric sequence and (x,y,9) is arthemetic sequence then..evaluate the value of x,y and find Gn
Answer by ikleyn(52787)   (Show Source): You can put this solution on YOUR website!
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if (x,y,12) is decreasing geometric sequence and (x,y,9) is arthemetic sequence then..evaluate the value of x,y and find Gn
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1.  Since (x,y,12)  is a geometric sequence, you have

        = ,   or   = .   (1)


2.  Since (x,y,9)  is an arithmetic sequence, you have

       y - x = 9 - y,   or   2y = 9 + x   (2)


3.  From (2), express x = 2y-9 and substitute it into (1). You will get

        = 12*(2y-9),   or

        = .

    The solutions are y = 6 and/or 18.


4.   a) If y = 6, then the first progression (GP) is  (3, 6, 12) and the second progression (AP) is  (3, 6, 9).

     b) If y = 18, then the first progression (GP) is  (27, 18, 12) and the second progression (AP) is  (27, 18, 9).


5.   Since the GP is decreasing, it leaves only one answer: b)

These two lessons in this site
    - One characteristic property of arithmetic progressions
    - One characteristic property of geometric progressions
helped me to quickly solve the problem.


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