Q.

a(1b+1c), b(1c+1a), c(1a+1b)  are in AP, then

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a

1a,1b,1c  are in AP.

b

a,b,c  are in HP

c

1a,1b,1c  are in GP

d

a,b,c  are in AP.

answer is D.

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Detailed Solution

Given, a(1b+1c), b(1c+1a), c(1a+1b)  are in AP.⇒               a(b+c)bc,b(c+a)ca,c(a+b)ab are in AP.⇒ab+acbc+1,bc+abac+1,ca+cbab+1 are in A.P  ⇒ab+bc+cabc,ab+bc+caac,ab+bc+caab are in A.P   ⇒  1bc,1ac,1ab  are in A.P   ⇒a , b ,c are in A.P
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a(1b+1c), b(1c+1a), c(1a+1b)  are in AP, then