Sequence And Series Question 311
Question: If $ a,b,c $ are three unequal numbers such that $ a,b,c $ are in A.P. and b - a, c - b, a are in G.P., then a : b : c is
[UPSEAT 2001]
Options:
A) 1 : 2 : 3
B) 2: 3 : 1
C) 1 : 3 : 2
D) 3 : 2 : 1
Show Answer
Answer:
Correct Answer: A
Solution:
a, b, c are in A.P.
Þ a + c = 2b ….(i) Also, $ b-a,c-b,a $ are in G.P.
Þ $ {{(c-b)}^{2}}=(b-a)a $
Þ $ (b-a)(c-b)=(b-a)a $ $ (\because c-b=b-a $ as a, b, c are in A.P.)
Þ $ c-b=a $ $ (\because a\ne b) $
Þ $ b=c-a $ ?..(ii) From (i) and (ii), $ a=\frac{b}{2}\text{ and }c=\frac{3b}{2} $ \ $ a:b:c::\frac{b}{2}:b:\frac{3b}{2} $
Þ $ a:b:c::1:2:3 $ .
BETA
