2002 grand prix gt 3800 II engine 115,000 now putting over 2,000 miles a month on open road Problem? I am starting to put a quart of oil in every month, around 2,000 miles and change oil and filter at 5,000 to 6,000 miles; I see no leaks under car, on engine, around oil filter, no smoke from exhaust; what coyuld be causing this?

Most common cause of that is dried out valve stem seals. You could try adding a VI improver like lucas engine treatment. One quart every 2000 miles is not terrible but is a bit on the excessive side.
You may want to change the brand and rating of the oil you are presently using. (if you are using a 10w anything, go to a 20w as the first number) Some oils burn off faster than others. I'd even consider using a good synthetic as synthetics resist burn off and do not react to internal shear forces anywhere as fast as normal lubricants do.
If the problem continues, the only real option is to replace the seals which is a fairly big job.

Check the pcv valve, it will **** up oil and burn it if bad, and also check the hose to pcv valve. depending on vehicle the price for a pcv valve is very reasonable. pull out pcv valve and shake it ! if it rattles its ok. but if not replace it. have a good day !! ( positive crankcase ventilation ).