Do i qualify for the 72 hour free transit in Beijing?

I am a US citizen flying from Orlando Florida to Seoul. After I arrive to Seoul, I want to go from Seoul to Beijing and then back to Seoul. I would be only three days in Beijing (weekend trip). My itinerary would be Orlando-Seoul, then Seoul-Beijing-Seoul, and then after a few days in Seoul back to Orlando. Or is there a way to get the visa or permit at my arrival to Beijing? Thank you.