Welcome! I hope you get it working the way you'd like. Have you considered an ARRAYFORMULA?
Try pasting that into a cell with 10 blank cells under it. It only goes to 10 dates for this example, but it could be whatever length you choose. Array formulas are great because they do your requested calculations and operations on a whole incoming set of cells or values, rather than just for the single cell they occupy. I'm typing this out in painful detail for clarity, but nobody reading this should be intimidated—they're easy to use once one becomes familiar with them.
+ ( ROW(1:10) -1 ) *7
In english, in order of how it's calculated:
means to do the contained formula over and over to cover all the incoming data.
as you know, DATE just generates a date in the format Sheets then understands.
Your example contained an increasing list of 7's multiples. That's the final thing we need here too; your 7, 14, 21… "addends" list. But we don't want to have to type them out, or even drag them down, so here I'm using a common trick and asking Sheets' ROW function to output "the row number of the first ten rows".
No surprises—the row numbers of the first ten rows are just the numbers 1 to 10. Since that's a whole array of numbers though, the ARRAYFORMULA will do the math once for each integer 1 through 10.
One detail needs addressing; we can think of your list as actually starting by adding 0 days to the first day—we don't want to add a week to the first date. So here we don't want 1 to 10; we want to add 0 to 9. So for each repetition, it
-1 subtracts one from the current number.
Finally, we multiply that times seven
*7, so our list 0, 1, 2… becomes 0, 7, 14…
That list, 0 through 63 is then added to the DATE you chose, with one output cell for each input number. So to generate, say 52 weeks worth, you'd just change it to
It all 'lives' in one cell, you can change it in just that one spot in the future, it's flexible, it's automatic, and it's very quick even for huge output sets. I hope I haven't scared you or anyone else off—ARRAYFORMULAs are an amazing tool.