SOLUTION: The first term of a G.P is x and 3rd term is y. Find an expression for the common ratio in terms of x and y. the 1st and 3rd term of a G.P are 8 and 18 respectively and the com

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Question 1189826: The first term of a G.P is x and 3rd term is y. Find an expression
for the common ratio in terms of x and y. the 1st and 3rd term of
a G.P are 8 and 18 respectively and the common ratio is positive,
find the common ratio.
Found 2 solutions by ikleyn, Edwin McCravy:
Answer by ikleyn(52788)   (Show Source): You can put this solution on YOUR website!
.
(a) the first term of a G.P is x and 3rd term is y. find an expression for the common ratio in terms of x and y.
(b) the 1st and 3rd term of a G.P are 8 and 18 respectively and the common ratio is positive, find the common ratio
~~~~~~~~~~~~~~~~~


                        Part (a) 


     = x;    = y = .


    So,  y = x*r^2,  which gives  for the common ratio  r = +/- .      ANSWER



    Notice that this formula for the common ratio "r" works in real numbers  IF and only IF  

    the ratio   is non-negative, which means that both x and y must be of the same sign, and both are not zero.


                        Part (b) 


     = 8;    = 18 =  = .


    It gives  r =  =  = +/- .      


    Since the condition says that common ratio is positive, 

    it leaves only one option for the common ratio  r =  = 1.5.   ANSWER

Solved.



Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
the first term of a G.P is x and 3rd term is y.
Find an expression for the common ratio in terms ]
of x and y.
So the sequence is like this
__x__, ___, __y__,...




The 1st and 3rd term of a G.P are 8 and 18 respectively
and the common ratio is positive, find the common ratio.
Plug in x=8 and y=18 in that and solve for r, using only 
the + of ±.

Edwin
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