Lawn mower running a little rough.?

I bought a used push mower last night. It starts great on the first pull, but it cycles when it's running, it speeds up and slows down. I added a little bit of fuel stabilizer to the gas, to see if that would help and it didn't. Wondering what the fix is here, I'm sure it's some type of carb problem, but I don't know anything about motors and working on them? Is there any fuel additive or something I can run through it to clear it out? Thank you very much!