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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-> 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
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
