First slide

Geometric progression

Question

Suppose $a, b, c$ are positive and form an increasing G.P. If $a + b + c = x b$ , then

Moderate

A

$x > 3$
B

$x > 4$
C

$x > \sqrt{5}$
D

$x > \sqrt{3} + \sqrt{5}$

Solution

If $r > 1$ is the common ratio of the G.P., then
$\frac{b}{r} + b + b r = x b \Rightarrow x - 1 = r + \frac{1}{r} > 2$

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