Sequence And Series Question 275
Question: If $ a,\ b,\ c $ are in A.P., then $ {10^{ax+10}},\ {10^{bx+10}},\ {10^{cx+10}} $ will be in
[Pb. CET 1989]
Options:
A) A.P.
B) G.P. only when $ x>0 $
C) G.P. for all values of $ x $
D) G.P. for $ x<0 $
Show Answer
Answer:
Correct Answer: C
Solution:
$ a,\ b,\ c $ are in A.P.
$ \Rightarrow $ $ 2b=a+c $ Now $ {{({10^{bx+10}})}^{2}}=({10^{ax+10}}.\ {10^{cx+10}}) $
$ \Rightarrow $ $ {10^{2(bx+10)}}={10^{ax+cx+20}} $
$ \Rightarrow $ $ 2(bx+10)=ax+cx+20,\ ,x $
$ \Rightarrow $ $ 2b=a+c\ \ i.e.\ \ a,\ b,\ c $ are in A.P. Hence these are in G.P. $ \forall x $ . Note: As we know if $ a,\ b,\ c $ are in A.P., then $ {x^{an+r}},\ {x^{bn+r}},\ {x^{cn+r}} $ are in G.P. for every $ n $ and $ r $ .
BETA
