What are #3# geometric means between #1# and #25# ?

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Answer 1 · 2017-11-25T16:44:13

#sqrt(5)#, #5# and #5sqrt(5)#

The geometric mean of #2# positive numbers #a# and #b# is #sqrt(ab)#

So the geometric mean of #1# and #25# is #sqrt(1 * 25) = sqrt(25) = 5#

The geometric mean of #1# and #5# is #sqrt(1 * 5) = sqrt(5)#

The geometric mean of #5# and #25# is #sqrt(5 * 25) = 5sqrt(5)#

So the sequence:

#1#, #sqrt(5)#, #5#, #5sqrt(5)#, #25#

is a geometric sequence.

The common ratio is #sqrt(5)#.