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Question

If ln(a+c) , ln(a-c) , ln(a-2b+c) are in A.P, then


A

a,b,c are in A.P.

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B

a2,b2,c2 are in A.P.

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C

a,b,c are in G.P.

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D

a,b,c are in H.P.

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Solution

The correct option is D

a,b,c are in H.P.


In(a+c), ln(ac), ln(a2b+c) are in A.P.a+c,ac,a2b+c are in G.P.(ca)2=(a+c)(a2b+c)(ca)2=(a+c)22b(a+c)2b(a+c)=(a+c)2(ca)22b(a+c)=4acb=2aca+c
a,b,c are in H.P.


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