If ${log}_{10} a, {log}_{10} b, {log}_{10} c$ 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.
Since ${log}_{10} a, {log}_{10} b, {log}_{10} c$ are in AP
$2 {log}_{10} b = {log}_{10} a + {log}_{10} c$
${log}_{10} b^{2} = {log}_{10} a c$
$b^{2} = a c$
a,b,c are in GP

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