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# Insert two geometric means between 4 and 256 .

$\begin{array}{1 1} 8,16 \\ 32,128 \\ 16,128 \\ 16,64 \end{array}$

Explanation : $4,g_{1},g_{2},256\; are\;in\;GP$
$4,4r,4r^2,256.$
$4\;.r^3=256$
$r^3=\large\frac{256}{4}=64\quad \;r=4$
$GM=4r\;\xi\;4r^2=4*4\;\xi\;4*4*4$
$=16\;\xi\;64.$
edited Jan 24, 2014