How do you write a sequence that has three geometric means between 256 and 81?

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Answer 1 · 2015-11-20T23:39:32

#256, 192, 144, 108, 81#

#256=4^4# and #81 = 3^4#

So the geometric mean of #256# and #81# is:

#sqrt(256*81) = sqrt(4^4*3^4) = 4^2*3^2 = 144#

The geometric mean of #256# and #144# is:

#sqrt(256*144) = sqrt(4^4 4^2 3^2) = 4^3*3 = 192#

The geometric mean of #144# and #81# is:

#sqrt(144*81) = sqrt(4^2 3^2 3^4) = 4*3^3 = 108#

The sequence: #256, 192, 144, 108, 81# is a geometric sequence with common ratio #3/4#