Question

If a, b, c are in A.P., b-a, c-b and a are in G.P., then a:b:c is (a) 1:2:3 (b) 1:3:5 (c) 2:3:4 (d) 1:2:4

Answer 1

Given:-

a,b,c are in A.P.

b-a,c-b,a are in G.P.

To Find:-

a:b:c = ?

Solution:-

In A.P.

$(b - a) = (c - b) - - - - (1)$

And in G.P.

${(c - b)}^{2} = a(b - a)$

${(b - a)}^{2} = a(b - a).$

$b - a = a$

$b = 2a$

$now.$

${(c - b)}^{2} = a(b - a)$

${(c - b)}^{2} = a(c - b)$

$c - b = a$

$as \: \: b = 2a$

$therfore \\ c = 2a + a$

$c = 3a$

$thereore$

a : b : c

a : b : c = a : 2a : 3a

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

a : b : c = a : 2a : 3a= 1 : 2 : 3.so it is your solutions..

Thank you.