72-Hour Free Transit for two nights' stay in Beijing

I'm a US citizen. I am going to join a 11 days tour Thailand and Beijing, our tour will end in Beijing and stay over in Beijing for 2 nights to enjoy the 72-Hour Visa-Free before the groups fly back to the US. Do I need to apply for a Visa if I fly to Seoul (South Korea) on the same day our group leaves for the U.S. and I'll back to Beijing Airport 7 days later to transit to leave for the U.S.?