If $l o g_{10} a, l o g_{10}, l o g_{10} c$ are in A.P., then $a, b, c$ must be in

A.P.

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G.P.

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H.P.

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None of these

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Solution

The correct option is B G.P.
If $l o g_{10} a, l o g_{10} b, l o g_{10} c$ are in A.P., then

$2 l o g_{10} b = l o g_{10} a + l o g_{10} c$

$l o g_{10} b^{2} = l o g_{10} a c$

$b^{2} = a c$ , this is the condition for variables to be in G.P.

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