If a,b, c are in AP, b - a, c - b and a are in GP, then a : b : c is

If a,b, c are in AP, b – a, c – b and a are in GP, then a : b : c is

(1) 1 : 2 : 3

(2) 1 : 3 : 5

(3) 2 : 3 : 4

(4) 1 : 2 : 4

Solution:

Since a, b c are in AP

(b – a) = ( c- b) … (i)

b – a, c – b and a are in GP

So (c – b)² = (b-a) a

From (i)

(b – a)² = (b-a) a

(b – a) = a

2a = b

From (i)

(c – b)² = ( c- b) a

(c- b) = a

c = a+b …(ii)

Put value of b in (ii)

c = a+ 2a

c = 3a

So a: b : c = a : 2a : 3a = 1 : 2 : 3

Hence option (1) is the answer.