First slide

Harmonic Progression

Question

If a, b, c are real and in A.P. and $a^{2}, b^{2}, c^{2}$ are in H.P., then

Moderate

A

$a = b = c$
B

$2 b = 3 a + c$
C

$b^{2} = \sqrt{a c / 8}$
D

$a b = c$

Solution

$2 b = a + c & b^{2} = \frac{2 a^{2} c^{2}}{a^{2} + c^{2}}$
$Simplify, we get a = 3, b = 3, c = 3$

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