Insert three geometric means between $1$ and $256$ .

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Solution

Let $G_{1}, G_{2}, G_{3}$ be 3
GMS both 1, & 256
then
$1, G_{1}, G_{2}, G_{3},$ 256 will be in GP
Let common ratio be r
$∴ G_{1} = r$
So $r^{4} = 256$
$r = \pm 4$
$G_{1} = \pm 4$
$G_{2} = \pm 16$
$G_{3} = \pm 64$

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