Question

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

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.