I do not think it will come even remotely close to Red's first week sales. I do however think it will be a significantly larger debut than Yours Truly simply based on the fact that
A) She is a more established artist
B) This era is doing exceptionally better than her yours truly era. I mean problem debuted with 420k first week and it's expected to sell 70k more copies this week (4th week) than "The Way" did in its opening week! It was Platinum in like its 3rd or 4th week (faster than The Way went GOLD) keeping in mind that Problem is one of Ariana's weakest songs it seems to me people are only buying it because of Ariana and her radio support.
C) Her audience has drastically expanded, she appeals to gay, straight, black, and white audiences *she took notes on MiMi clearly

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Like I said its too early on in her career to be pulling those Taylord numbers, but maybe her 4th Album. I see her debuting with 250-400k depending on her second single