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Sum of n Terms

If a, b, c ...

Question

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

1 : 2 : 3

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1 : 3 : 5

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2 : 3 : 5

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1 : 2 : 4

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Solution

The correct option is A $1 : 2 : 3$
Given, $a, b, c$ are in AP and $b - a, c - b, a$ are in GP.
Therefore, $2 b = a + c$ and $(c - b)^{2} = (b - a) a$
$\Rightarrow (b - a)^{2} = (b - a) a$
$\Rightarrow b = 2 a$
$\Rightarrow c = 3 a$
Thus, $a : b : c = 1 : 2 : 3$ .

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