Sequence And Series Question 319
Question: If arithmetic mean of two positive numbers is $ A $ , their geometric mean is $ G $ and harmonic mean is $ H $ , then $ H $ is equal to
[MP PET 2004]
Options:
A) $ 1.2+2.3+3.4+4.5+……… $
B) $ \frac{G}{A^{2}} $
C) $ \frac{A^{2}}{G} $
D) $ \frac{A}{G^{2}} $
Show Answer
Answer:
Correct Answer: A
Solution:
Let the positive number $ a_1 $ and $ a_2 $ $ a_1,,A,,a_2 $ ????A.P. then $ A=\frac{a_1+a_2}{2} $ $ G^{2}=AH $ ????.G.P. $ G=\sqrt{a_1a_2} $ $ \frac{1}{a_1},,\frac{1}{H},,\frac{1}{a_2} $ ??..H.P. $ \frac{2}{H}=\frac{1}{a_1}+\frac{1}{a_2} $ ; $ H=\frac{2a_1a_2}{a_1+a_2} $ ; $ H=\frac{G^{2}}{A} $
BETA
