How do you find two geometric means between 5 and 135?

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Answer 1 · 2015-11-25T00:13:46

We are effectively looking for $a$ and $b$ such that $5$ , $a$ , $b$ , $135$ is a geometric sequence.

This sequence has common ratio $root(3)(135/5) = 3$ , hence $a = 15$ and $b=45$

In a geometric sequence, each intermediate term is the geometric mean of the term before it and the term after it.

So we want to find $a$ and $b$ such that $5$ , $a$ , $b$ , $135$ is a geometric sequence.

If the common ratio is $r$ then:

$a = 5r$

$b = ar = 5r^2$

$135 = br = 5r^3$

Hence $r^3 = 135/5 = 27$ , so $r = root(3)(27) = 3$

Then $a = 5r = 15$ and $b = ar = 15*3 =45$