Question
If a, b, c, d are in H.P., then ab + bc + cd is equal to
Answer: Option A
:
A
Since a, b, c, d are in H.P., therefore b is the H.M. of a and c
i.e., b = 2acb+d, ∴(a+c)(b+d) = 2acb.2bdc
⇒ab+ad+bc+cd = 4ad ⇒ab+bc+cd = 3ad
Trick : Check for a =1, b = 12, c = 13, d = 14
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:
A
Since a, b, c, d are in H.P., therefore b is the H.M. of a and c
i.e., b = 2acb+d, ∴(a+c)(b+d) = 2acb.2bdc
⇒ab+ad+bc+cd = 4ad ⇒ab+bc+cd = 3ad
Trick : Check for a =1, b = 12, c = 13, d = 14
Was this answer helpful ?
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