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

Question

Mathematics

Jenny Donaldson

1 May, 04:23

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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Answers (1)

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Tyson · Answer 1

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.