Sequence And Series Question 280
Question: Three non-zero real numbers form an A.P. and the squares of these numbers taken in the same order form a G.P. Then the number of all possible common ratios of the G.P. is
Options:
A) 1
B) 2
C) 3
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
Let the numbers be $ a-d,\ a,\ a+d $ . Then $ {{(a-d)}^{2}},\ a^{2},\ {{(a+d)}^{2}} $ are in G.P.
$ \therefore $ $ a^{4}={{(a-d)}^{2}}{{(a+d)}^{2}} $
$ \Rightarrow $ $ d^{4}-2a^{2}d^{2}=0 $
$ \Rightarrow $ $ d=0,\ \pm \sqrt{2}a $ Hence $ d $ has three values.
BETA
