Sequence And Series Question 205
Question: If $ a,\ b,\ c $ are in A.P. as well as in G.P., then
[MNR 1981]
Options:
A) $ a=b\ne c $
B) $ a\ne b=c $
C) $ a\ne b\ne c $
D) $ a=b=c $
Show Answer
Answer:
Correct Answer: D
Solution:
As given $ b=\frac{a+c}{2} $ ?..(i) and $ b^{2}=ac $ ?..(ii)
$ \Rightarrow {{(a+c)}^{2}}=4ac\Rightarrow {{(a-c)}^{2}}=0\Rightarrow a=c $ Putting $ a=c $ in (i), we get $ b=c $ ;
$ \therefore $ $ a=b=c $ .
BETA
