Which word, if inserted in the blank, makes the most sense in the context of the passage?

Your "ancestors" are your family members from hundreds of years ago, from whom you came to eventually be. So her ancestors must had dwelt there for generations , not days (atmost, days would mean 15 or 20 days) and not seasons (a year has 4 seasons, so 3 seasons wouldn't even make a whole year). And infinity doesn't make sense at all, we don't measure time by infinity. Meanwhile, a generation typically has 20-30 years, hence it's the correct option.