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

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241.
If a, b, c are in AP, b - a, c - b and a are in GP, then a: b : c is

1 : 2 : 3

1 : 3 : 5

2 : 3 : 4

1 : 2 : 4

A.

1 : 2 : 3

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

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