First slide

Geometric progression

Question

If $a, b, c$ are in H.P. then $a - \frac{b}{2}, \frac{b}{2}, c - \frac{b}{2}$ are in

Moderate

A

A.P.
B

G.P.
C

A.G..P
D

H.P.

Solution

$b = \frac{2 a c}{a + c},$ and
$\begin{aligned} (a - \frac{b}{2}) (c - \frac{b}{2}) = a c - \frac{b}{2} (a + c) + \frac{b^{2}}{4} \\ = a c - a c + \frac{b^{2}}{4} = \frac{b^{2}}{4} \end{aligned}$

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