I'm a sports fan, I like playing football and play tennis.这句

I'm a sports fan, I like playing football and play tennis.这句有两个play,第一个是playing而
第二个是play,为什么?前几天作业上有道这样的题填空 I like sports.I like playing _ and play _.I am healthy and strong. 网上回答的人说是题出错了 应该是I like playing and playing.可我现在问的句子是在书上看到的,应该不会错啊!到底是怎样的?