If x,y and z are the first three terms of an geometric sequence, show that x^2,y^2 and z^2 form another geometric sequence

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asked Dec 20, 2017 226k views

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Eben Kadile · Answer 1 · 2017-12-24T12:37:39+0000

x y z are in geometric
x/y = y/z
OR y^2=xz

x^2, y^2, z^2

x^2, xz, z^2
If they are in geometric sequence then
xz/x^2 = z^2/xz
z/x = z/x
The ratios are common
so x^2,y^2 & z^2 is a GP.

If x,y and z are the first three terms of an geometric sequence, show that x^2,y^2 and z^2 form another geometric sequence

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