I have a 1997 geo metro with 74000 miles the service lite came on reverse quit working and now when the automatic transmission shifts it jurks
Service light may be due to the transmission problem. Reverse not working is a definite sign. Get the codes read. Autozone and some other auto parts stores will read them for free. This should at least let you know if it is a controller problem, or if you may need a transmission rebuild.
Well, since reverse is not electronically controlled, what I would first check is the fluid level then the linkages. If both are good then its time for the trans to come out and be torn down.
Scan the computer first, I am curious to see what code/s have been set.