2025 AMC 10B Problem 17

Consider a decreasing sequence of $n$ positive integers $x_1 > x_2 > \dotsb > x_n$ that satisfies the following two conditions:

$\qquad\bullet$ The average (arithmetic mean) of the first $3$ terms in the sequence is $2025.$

$\qquad\bullet$ For all $4 \leq k \leq n,$ the average of the first $k$ terms in the sequence is $1$ less than the average of the first $k - 1$ terms in the sequence.

What is the greatest possible value of ${n?}$