If a, b, c, d are in H.P., then ab + bc + cd is equal to
3ad
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