Question 17
Consider a decreasing sequence of $n$ positive integers $x_1 \gt x_2 \gt x_3 \gt \cdots \gt x_n$ that satisfies the following conditions. The average of the first $3$ terms in the sequence is $2025.$ For all $4 \le k \le n,$ 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 $n?$
What is the greatest possible value of $n?$