Sequence And Series Question 335
Question: The product of three geometric means between 4 and $ \frac{1}{4} $ will be
Options:
A) 4
B) 2
C) $ -1 $
D) 1
Show Answer
Answer:
Correct Answer: D
Solution:
We have $ 4,\ g_1,\ g_2,\ g_3,\ \frac{1}{4} $ is a G.P. Here $ a=4 $ , $ g_1=ar=4\times r,\ \ \ g_2=ar^{2},\ \ \ g_3=ar^{3} $ and $ g_4=ar^{4}=4\times r^{4}=\frac{1}{4} $
$ \Rightarrow r^{4}=\frac{1}{16}={{( \frac{1}{2} )}^{4}}\Rightarrow r=\frac{1}{2} $ Now product of three G.M. $ g_1.\ g_2.\ g_3=ar.\ ar^{2}.\ ar^{3} $ $ =a^{3}r^{6}=4^{3}\times {{( \frac{1}{2} )}^{6}}=\frac{4^{3}}{4^{3}}=1 $ . Note: The product of ? $ n $ ? geometric means between ? $ a $ ? and $ \frac{1}{a} $ is always equal to 1.
BETA
