Sequence And Series Question 184
Question: If the arithmetic, geometric and harmonic means between two positive real numbers be $ A,\ G $ and $ H $ , then
[AMU 1979, 1982; MP PET 1993]
Options:
A) $ A^{2}=GH $
B) $ H^{2}=AG $
C) $ G=AH $
D) $ G^{2}=AH $
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Answer:
Correct Answer: D
Solution:
Let $ A=\frac{a+b}{2},\ G=\sqrt{ab} $ and $ H=\frac{2ab}{a+b} $ . Then $ G^{2}=ab $ …..(i) and $ AH=( \frac{a+b}{2} )\ .\ \frac{2ab}{a+b}=ab $ …..(ii) From (i) and (ii), we have $ G^{2}=AH $ .
BETA
