I sat there to listen to music和I sat there listening to musi

楼上正解.
listening to the music表伴随状态.
再问： I went to outside to buy icecream.可以吗？
再答： 嗯。不定式一般表目的。变成了我坐下为了听音乐。显然不如我坐在地上听着音乐合理一些嘛。 其实语法上没错，只是不如后者合理。