Sequence And Series Question 6
If $ a,\ b,\ c,\ d $ are in A.P., then $ ab+bc+cd $ is equal to
Options:
A) $ 3ad $
B) $ (a+b)(c+d) $
C) $3ac$
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
Since $ a,\ b,\ c,\ d $ are in H.P., therefore $ b $ is the H.M. of $ a $ and $ c $ $ i.e. $ $ b=\frac{2ac}{a+c} $ and $ c $ is the H.M. of $ b $ and $ d $ $ i.e. $ $ c=\frac{2bd}{b+d} $ . $ \therefore $ $ (a+c)(b+d)=\frac{2ac}{b} \cdot \frac{2bd}{c} $ $ \Rightarrow $ $ ab+ad+bc+cd=2ad+2bc $ $ \Rightarrow $ $ ab+bc+cd=3ad $ . Trick: Check for $ a=1,\ b=\frac{1}{2},\ c=\frac{1}{3},\ d=\frac{1}{4} $ .
BETA
