Explanation

(c)
Since, $\frac{1}{b - a} + \frac{1}{b - c} = \frac{1}{a} + \frac{1}{c}$
$\Rightarrow \frac{b - a + b - c}{b^{2} - (a + c)b + ac} = \frac{a + c}{ac}$
$\Rightarrow 2abc - (a + c)ac = b^{2}(a + c) - b(a + c)^{2} + ac(a + c)$
$\Rightarrow 2ac(b - a - c) = b(a + c)(b - a - c)$
$\Rightarrow \frac{2ac}{a + c} = b$
$\Rightarrow a,b,c$ are in HP.