If the system of linear equations $x+2ay+az=0,x+3by+bz=0,x+4cy+cz=0$ has a non-zero solution the a,b,c

Question

$\begin{array}{1 1}(a)\;Satisfy \;a+2b+3c=0\\(b)\;are\;in\;H.P\\(c)\;are\;in\;G.P\\(d)\;are\;in\;H.P\end{array}$