Sequence And Series Question 305
Question: If $ \frac{a}{b},\frac{b}{c},\frac{c}{a} $ are in H.P., then
[UPSEAT 2002]
Options:
A) $ a^{2}b,,c^{2}a,,b^{2}c $ are in A.P.
B) $ a^{2}b,,b^{2}c,,c^{2}a $ are in H.P.
C) $ a^{2}b,,b^{2}c,,c^{2}a $ are in G.P.
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
$ \frac{b}{a},\frac{c}{b},\frac{a}{c} $ are in A.P.
Þ $ \frac{2c}{b}=\frac{b}{a}+\frac{a}{c} $
$ \Rightarrow \frac{2c}{b}=\frac{bc+a^{2}}{ac} $
Þ $ 2ac^{2}=b^{2}c+ba^{2} $
$ \therefore ,a^{2}b,,c^{2}a $ and $ b^{2}c $ are in A.P.
BETA
