I know the hydrostat transmission if from Hydro Gear. I have read many problems with it slipping. I can't find the model number, but looks to be a LT or GT series. Where do I find which series and model?

Most Sears tractor have a white sticker on the body under the flip up seat.

Ballengerb is correct, there should be a sticker somewhere with a number e.g. 917.12334556747