In the first Thanksgiving episode, or "Turkey Day" as Boyle calls it, we see Jake totally avoiding being a part of it. He even refuses to go to Amy's Thanksgiving dinner and wishes to spend the night working instead
Jake convinces Captain Holt to take charge of the next case that arrives, in order not to attend the Thanksgiving Party. And when that happens, he happily tags along the Captain
Before the episode ends, Jake reveals why he hates Thanksgiving so much. It was because of his parent's absence and how he had to spend all his childhood Thanksgivings alone, eating only sandwiches
Finally however, Captain Holt explains to Jake how "nine-nine" is his new family now. And that he'll have to accept past memories so that he can move on with better ones. Finally at the end of the episode, we see Jake joining everyone and having a great Thanksgiving feast.
In another Thanksgiving episode which also shows Jake's refusal of the day, the shows ends with Jake finally celebrating the day with the whole 'Nine-Nine' fam and ending the day with a toast.