If $x, 2 x + 2, 3 x + 3$ are in G.P., then $5 x, 10 x + 10, 15 x + 15$ form

An A.P.

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A g.P.

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A constant sequence

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Neither A.P. nor a G.P.

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Solution

The correct option is A A g.P.
We are given $x, 2 x + 2, 3 x + 3$ are in G.P.
Let $a = x, b = 2 x + 2, c = 3 x + 3$
$\Rightarrow a, b, c$ are in G.P.
Therefore $b^{2} = a \times c$
We are asked about relation between $5 a, 5 b, 5 c$ .
${(5 b)}^{2} = 25 b^{2}$
$5 a \times 5 c = 25 a c = 25 b^{2}$
$\Rightarrow {(5 b)}^{2} = 5 a \times 5 c$
Therefore, it is a G.P.
Hence, option B is correct.

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