First slide

Geometric progression

Question

Let a,b,c form a G.P of common ratio r, with 0<r<1. If a,2b,3c forms an A.P, then common ratio r is

Moderate

A

$\frac{1}{2}$
B

$\frac{1}{3}$
C

$\frac{2}{3}$
D

$\frac{1}{4}$

Solution

$b = {ar}_{}, c = {ar}^{2}, 0 < c < 1$
$\begin{array}{l} a, 2 b, 3 c form an A.P \\ 4 b = a + 3 c \\ 4 ar = a + 3 {ar}^{2} \\ \to 3 r^{2} - 4 r + 1 = 0 \\ \to r = 1 / 3 \end{array}$

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