Question 1044745: If three geometric means are inserted between 120 and 15/2,find the third of these geometric means
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! If  geometric means are inserted between  and  , those five numbers form a geometric sequence.
Also, all five terms are positive, meaning that so is the common ratio.
If  ,  ,  , 
, and  .
So,
 <--> <--> <-->
The thirds of those geometric means can be calculated as
 ---> ---> ,
or more easily as  .
Alternatively, we can calculate the geometric mean of and ,
which would be the second of the three means to be inserted, as
 .
Then we can calculate the third of the three means to be inserted as the geometric mean of  and ;
 .
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