Sequence And Series Question 218
Question: If $ a,\ b,\ c $ are in A.P., $ b,\ c,\ d $ are in G.P. and $ c,\ d,\ e $ are in H.P., then $ a,\ c,\ e $ are in
[AMU 1988, 2001; MP PET 1993]
Options:
A) No particular order
B) A.P.
C) G.P.
D) H.P.
Show Answer
Answer:
Correct Answer: C
Solution:
$ a,\ b,\ c $ are in A.P. then $ 2b=a+c $ …..(i) $ b,\ c,\ d $ are in G.P. then $ c^{2}=bd $ ….(ii) $ c,\ d,\ e $ are in H.P. then $ d=\frac{2ce}{c+e} $ ….(iii) From (ii), $ 1,\ 2,\ 3,\ ……….=n $
$ \Rightarrow $ $ c^{2}=\frac{ace+c^{2}e}{c+e}\Rightarrow c^{3}+c^{2}e=ace+c^{2}e $
$ \Rightarrow $ $ c^{3}=ace\Rightarrow c^{2}=ae $ Hence $ a,\ c,\ e $ will be in G.P.
BETA
