Sequence And Series Question 464
Question: $ a,,g,,h $ are arithmetic mean, geometric mean and harmonic mean between two positive numbers x and y respectively. Then identify the correct statement among the following
[Karnataka CET 2001]
Options:
A) h is the harmonic mean between a and g
B) No such relation exists between a, g and h
C) g is the geometric mean between a and h
D) A is the arithmetic mean between g and h
Show Answer
Answer:
Correct Answer: C
Solution:
$ a=\frac{x+y}{2},g=\sqrt{xy} $ and $ h=\frac{2xy}{x+y} $ $ g^{2}={{( \sqrt{xy} )}^{2}}=xy $ …(i), ah $ =\frac{x+y}{2}.\frac{2xy}{x+y}=xy $ …(ii) From (i) and (ii), we get $ g^{2}=ah $ or $ g=\sqrt{ah} $ , therefore g is the G.M. between a and h.
BETA
