Connect alpine 7874 to alpine powered sub

You need to run the RCA cables from the head unit to the sub for the audio signal, and possibly a turn on wire (the blue one on the back of the head unit), unless the sub has an automatic power feature.

The sub also needs power and ground wires attached, but those do not connect to the head unit. Power should be run directly from the battery with an inline fuse, and ground should go to the nearest good ground point (Trunk latch, seat bolt, etc).