2004 Chevy Silverado SS 5.3 L
This is probably a dumb question that I may have all the information on in the first place. But, I'm not a auto mechanic so I figured why not run it past some more experienced people and see what they say.

My truck sat for about a week while I was using my wife's car to job hunt. One day I went out to get something and I noticed the lights were very dim (obvious sign of a low battery). I tried to start it and indeed the battery was almost dead. I gave it a jump and let it run for about 20 min (I didn't need to go anywhere) and shut it off. I checked it later that day and it started right up. 3 days later I needed to go somewhere and decided to get the truck out. Battery was dead again. At this point I'm just thinking the battery needs replaced because it's not holding a charge for very long. I jumped it and let it run for about 15 minutes. I went to leave and noticed that when I put it in drive the engine idle got very low. I took out of the driveway and at the end of my driveway is a small hill. When I took off of that the truck died. I parked it and took the car. Yesterday (2 days after) I went out and the truck (to my surprise) started right up as if it had plenty of juice. I figured it would need a jump again. But, it's still doing the same very low wanting to die idle and I'm afraid to drive it. I'm in no big hurry but tight on money and don't want to go through a bunch of parts troubleshooting unless I have to. Does this sound more like an alternator problem then a battery problem? Can a low battery cause the truck to idle low and die?
Any advice is helpful and I hope I'm not wasting anyone's time here.