Sequence And Series Question 277
Question: $ {\log_3}2,\ {\log_6}2,\ {\log_{12}}2 $ are in
[RPET 1993, 2001]
Options:
A) A.P.
B) G.P.
C) H.P.
D) None of the above
Show Answer
Answer:
Correct Answer: C
Solution:
If the numbers are $ \frac{1}{x},\ \frac{1}{y},\ \frac{1}{z} $ , then $ x={\log_2}3,\ y={\log_2}2\ .\ 3=1+{\log_2}3 $ and $ z=2+{\log_2}3 $ . Therefore $ =\frac{1.(10^{91}-1)}{10-1}=\frac{{{(10^{13})}^{7}}-1}{10^{13}-1}\times \frac{10^{13}-1}{10-1} $ are in A.P. Hence $ \frac{1}{x},\ \frac{1}{y},\ \frac{1}{z}\ \ \ i.e. $ , the given numbers are in H.P.
BETA
