Swedes have good personal qualities. They can be generous and welcoming. Plus, many Swedish people have a good memory.
In combination this means, Swedes can remember that you invited them for a beer, even if it's a while ago and that they haven't invited you back since. This kind of story rarely happens in Sweden though, and if it does, expect your Swedish friend feeling guilty or even anxious not having invited you back yet.
Invitation from a Swede
When you're out for drink with a Swede, it's completely fine if you invite them for a beer. But have a look at their face when you speak out the invitation – saying to the personell you pay the bill – your Swedish friend will make the same expression as a student trying to memorize vocabulary. What your friend tries to remember is “Pay back a favor, worth amount x, as soon as possible”. If he won't have the chance to invite you to something that same evening, he will take care to equalize his debt next time you meet, even if that is just for a fika. You invited him for a beer in a Swedish pub before? Expect the best latte macchiatto with cream and syrup in return. Remember, alcohol is expensive in Sweden.
Or even if you drive along in your friend's car, you should offer to pay back half of the gasoline costs. This might sound weird in many countries but in Sweden this is completely normal. Even my closest Swedish friends, ask me how much they owe me after driving them to the city, a distance less than 5km.
It's important not to bother anyone. To not take without giving back.
On the first hand this might look like grasping, greediness, but it basically is just their believe to not end up in indebted relationships with others.
A way to reduce the feeling of guilt, in situations of receiving a favor, is to say thank you, a lot. “Tack, tack, tack-tack!”
So, dear new-Swede, if a Swede ever invites you for something, don't forget to return the favor within an appropriate time… say, the same evening or at the latest next time you meet for a fika.
In very urgent cases, say when you already know you're not going to see your friend for a while, consider saying to your friendly Swedish friend that you can “swisha tillbaks pengarna“, meaning “paying back with the money transfer app Swish”. Your friend will reply, “no, I invited you!” and he memorizes that you should pay time next time you're out together.
More ways to Swedishness, read the book: How to be Swedish – A Quick Guide to Swedishness – in 55 Steps, here on Amazon