If a, b, c are in AP then a bc , 1 c , 2 b are in

JEE Advanced Mathematics question

If are in AP then are in

(A)AP
(B)GP
(C)HP
(D)none of theseCorrect

Answer: (D)

Solution

Multiplying all three by (which does not change AP/GP/HP character) gives . - AP would need ; with this forces — impossible. - A counter-example settles GP/HP too:

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Question ID VK-107770