SOLUTION: Given that the first 5 terms of a geometric sequence are 3, x, 12, y, and 48, find, x and y. Assume both x and y are positive.

Question 1084079: Given that the first 5 terms of a geometric sequence are 3, x, 12, y, and 48, find, x and y. Assume both x and y are positive.
Answer by ikleyn(52817) (Show Source): You can put this solution on YOUR website!
.

1.  Finding x.  

    You have these two equations

    x = 3*r,   (1)   where "r" is unknown common ratio

    12 = x*r.  (2)


    Substitute (1) into (2). You will get  12 = (3*r)*r   or   12 =.

    It implies  =  = 4.   Hence, r = 2 or -2.

    
    It gives two solutions for x:  x = 3*2 = 6   and    x = 3*(-2) = -6.



2.  Finding y.

    You just found that there are two possibilities for the common ratio: r = 2  and  r = -2.

    At the first possibility,  y = 12^2 = 24.

    At the second possibility,  y = 12*(-2) = -24.

Answer. There are two solutions: (x,y): = (6,24) and (x,y) = (-6,-24).

Solved.

On geometric progressions, read the introductory lessons
    - Geometric progressions
    - The proofs of the formulas for geometric progressions
    - Problems on geometric progressions
    - Word problems on geometric progressions
    - Solved problems on geometric progressions

Also, you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Geometric progressions".

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