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  4. If a, b, c are in AP , b-a, c-b and a are in GP, then a: b: c is

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Q. If $a, b, c$ are in $AP , b-a, c-b$ and $a$ are in GP, then $a: b: c$ is

EAMCETEAMCET 2007

Solution:

Given, that, $2 b=a+ c$
and $(c-b)^{2}=(b-a) a$
$\therefore (b-a)^{2}=(b-a) a$
$\Rightarrow b=2 a$
$\Rightarrow c=3 a$
$\Rightarrow a: b: c=1: 2: 3$