If $\frac{\sin A}{\sin C}=\frac{\sin(A-B)}{\sin(B-C)}$, then the sides of ΔABC are in:

A.P. G.P. H.P. None of these

None of these

$\sin A . \sin (B - C) = \sin C \sin(A - B)$ $⇒ \sin(B + C) . \sin(B -C) = \sin(A - B) \sin(A + B) ⇒ \sin^2 B - \sin^2 C = \sin^2 A - \sin^2 B$ $⇒ a^2, b^2 c^2$ are in A.P. (using sin rule)