is the second date my responsibility now?

this might be a stupid question but i haven’t dated much so really don’t know. i (21f) went on a really fun date last weekend. i liked him a lot and he seemed to reciprocate. we’ve been texting since but he hasn’t offered to meet up this upcoming weekend or the next at all. maybe he’s just texting me back out of boredom? but also i’m wondering if it’s now like i’m the one who should offer a second date. is that how it works? a “back and forth” kind of deal? he put a lot of planning into our first date and it was pricey (i offered to split but he insisted on paying) which also makes me think he might not be keen on planning again. i really don’t know. i don’t mind being the one to offer and plan, but feel stupid asking if he’s only texting me out of boredom.