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

1 Answer
Nov 25, 2015

Answer:

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#

Explanation:

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#