Sequence And Series Question 521
Question: If $ A_1,,A_2 $ be two arithmetic means between $ \frac{1}{3} $ and $ \frac{1}{24} $ , then their values are
Options:
A) $ \frac{7}{72},,\frac{5}{36} $
B) $ \frac{17}{72},,\frac{5}{36} $
C) $ \frac{7}{36},,\frac{5}{72} $
D) $ \frac{5}{72},,\frac{17}{72} $
Show Answer
Answer:
Correct Answer: B
Solution:
Here $ \frac{1}{3},\ A_1,\ A_2,\ \frac{1}{24} $ will be in A.P., then $ A_1-\frac{1}{3}=\frac{1}{24}-A_2 $
$ \Rightarrow $ $ A_1+A_2=\frac{3}{8} $ ……(i) Now, $ A_1 $ is a arithmetic mean of $ \frac{1}{3} $ and $ A_2 $ , we have $ 2A_1=\frac{1}{3}+A_2\Rightarrow 2A_1-A_2=\frac{1}{3} $ ……(ii) From (i) and (ii), we get, $ A_1=\frac{17}{72} $ and $ A_2=\frac{5}{36} $ . Aliter : As we have formula $ A_{m}=a+\frac{m(b-a)}{n+1} $ where $ n=2,\ a=\frac{1}{3},\ b=\frac{1}{24} $
$ \therefore $ $ A_1=\frac{1}{3}+\frac{-7/24}{3}=\frac{17}{72} $ $ A_2=\frac{1}{3}+\frac{-14/24}{3}=\frac{10}{72}=\frac{5}{36} $
BETA
