If $$1a+1a$$−$$2b+1c+1c$$−$$2b=0$$ and a,b,c are not in A.P then:

Correct option is 4a,2b,c are in H.P

Questions

$If \frac{1}{a} + \frac{1}{a - 2 b} + \frac{1}{c} + \frac{1}{c - 2 b} = 0 and a, b, c are not in A.P then:$

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a,b,c are in G.P

a,b2,c are in A.P

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a,2b,c are in H.P

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detailed solution

Correct option is D

1a+1a−2b+1c+1c−2b=02(a−b)a(a−2b)+2(c−b)c(c−2b)=0a−ba(a−2b)+c−bc(c−2b)=0 Now, we can verify the result that a,2b,c are in H.P

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If 1a+1a−2b+1c+1c−2b=0 and a,b,c are not in A.P then:

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$If \frac{1}{a} + \frac{1}{a - 2 b} + \frac{1}{c} + \frac{1}{c - 2 b} = 0 and a, b, c are not in A.P then:$