First slide

Geometric progression

Question

$If a, b and c are in A.P, and b - a, c - b and a are in G.P, then a : b : c is$

Moderate

A

1:2:3
B

1:3:5
C

2:3:4
D

1:2:4

Solution

$\begin{array}{l} We have, \\ 2 b = a + c \\ (c - b)^{2} = (b - a) a \\ \Rightarrow (b - a)^{2} = (b - a) a [2 b = a + c \Rightarrow b - a = c - b] \\ \Rightarrow b = 2 a \\ \Rightarrow c = 3 a [using 2 b = a + c] \\ \Rightarrow a : b : c = 1 : 2 : 3 \end{array}$

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