Here's what you don't say:
- Do you need a Seder?
- Do you need a meal for YomTov?
- Which meals don't you have an invitation for?
- You can come for the first seder. Do you know who else needs a place for that night?
All of these things were said to me by well-meaning hosts and hostesses in the past.
Here's what you do say.
- Would you like to join us for the first seder?
- Would you like to join us for 2nd day lunch?
- Would you like to join us for any of the YomTov lunches, like any of the last days? You're welcome to bring a friend as well.
Remember, single people don't "need" meals, and if they do, it's rude to remind them of how much you have and how much they don't. As a former "older single" as well as a former divorcee, I can assure you that these words do hurt. Have a little sensitivity this YomTov, fill your tables with people who are currently alone, and treat them with sensitivity and respect.
(Getting off my soapbox now.)
Chag kasher v'sameach.