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Question

If 1bc, 1ca, 1ab be consecutive terms of an A.P., then (bc)2,(ca)2,(ab)2 will be in ___.


A

G.P

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B

A.P

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C

H.P

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D

None of these

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Solution

The correct option is B

A.P


If (bc)2,(ca)2,(ab)2 are in A.P.

Then we have (ca)2(bc)2 = (ab)2(ca)2

(ba)(2cab) = (c - b)(2a - b - c) ......(i)

Also if 1bc,1ca,1ab are in A.P.

Then 1ca1bc = 1ab1ca

b+a2c(ca)(bc) = c+b2a(ab)(ca)

(ab)(b+a2c) = (bc)(c+b2a)

(ba)(2cab) = (cb)(2abc)

Which is true by virtue of (i).


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