Question

$\text{If log (a + c) + log (a - 2b +c) = 2log(a -c), then a, b, c are in}$

• A. $H.P.$
• B. None of these
• C. $G.P.$
• D. $A.P.$

Answer 1

The correct option is A $H.P.$

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

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

$\Rightarrow a^2+b^2+2ac-2ab-2bc=a^2+c^2-2ac$

$\Rightarrow 4ac=2b(a+c)\Rightarrow b=\frac{2ac}{a+c}$