Question

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

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

Answer 1

Answer: (A)

$1:2:3$

Given, $a,b,c$ are in A.P. then $b-a=c-b$......(1).

Also given $b-a,c-b,a$ are in G.P.

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

Using (1) we get,

$(c-b)=a$

or, $c=a+b$......(2).

Using this in (1) we get,

$b-a=a$

or, $b=2a$

Using this value of $b$ in (2) we get,

$c=3a$.

So,

$a:b:c=a:2a:3a=1:2:3$. [ Using vales of $b,c$]