why wont my terrain go in reverse?

Could be a reverse solenoid but I have seen broken reverse bands cause the same problem. Time for a transmission shop to do some testing.

This seems odd for an eight year old transmission. If your transmission works properly in all forward gears but not in reverse, the problem could be that the transmission fluid is too low for it to function correctly. It's also possible that the fluid is dirty and has lost its ability to do its job. Change your fluid and if it's dark in color, your issue might be overheating, which can cause other defects, as well. When you shift an automatic transmission into reverse, the transmission position sensor tells the PCM to shift the transmission into reverse. If it doesn't, the sensor might be faulty. Also, a worn valve body might leak and create opposing pressures that inhibit shifting into reverse, but that's likely on only high mileage transmissions.