If $\large\frac{1}{x+y}$, $\large\frac{1}{xy}$, $\large\frac{1}{y+z}$ are in AP, $x, y, z$ are in

Question

$(a)\;AP\qquad(b)\;GP\qquad(c)\;HP\qquad(d)\;None\;of\;the\;above$