SOLUTION: If three geometric means are inserted between 120 and 15/2,find the third of these geometric means

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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