If $a,b,c$ are in AP. $b-a,c-b$ and a are in GP. then $a:b:c$ is

Question

$$\begin {array} {1 1} (a)\;1:2:3 & \quad (b)\;1:3:5 \\ (c)\;2:3:4 & \quad (d)\;1:2:4 \end {array}$$