How to send email distribution to only newly added members of a list?

Thank you in advance to anyone who can help. I'm looking for a way to email a survey invitation to a list of people that will grow each week, but only to those who have not already been sent an invitation to the survey. More details:
We have built a survey and our plan is to send it to a new group of people each week. Instead of creating a new distribution list each week, we would want to simply add the new survey recipients to the existing list. The part that I can't figure out is how to send the survey to only the people who have not been sent it yet. I see options to send the survey to the whole list and to individuals in the list.
Example: we start the list with 10 people and send the survey to them. The following week we add 8 people to the list, so there are 18 total people. After adding those 8 people, we only want to send the survey to those 8 people and not all 18 (we don't want the original 10 to get a second invitation).