Question

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

• A. 1:3:5
• B. 1:2:4
• C. 1:2:3
• D. 1:4:8

Answer 1

The correct option is C

1:2:3

Here b = $\frac{1}{2}$(a+c) and ${(c-b)}^2$ = a(b-a)

$\Rightarrow {[c-\frac{1}{2}(a+c\left)\right]}^2$ = a{ $\frac{1}{2}$(a+c) - a}

Since a $\ne$ c, c = 3a so b = 2a

$\therefore$ $\frac{a}{1}$ = $\frac{b}{2}$ = $\frac{c}{3}$ i.e., a : b : c = 1 : 2 : 3.