Question 14
Consider a decreasing sequence of $n$ positive integers $x_1 \gt x_2 \gt \cdots \gt x_n$ that satisfies the following two conditions:
• The average (arithmetic mean) 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 $n?$
• The average (arithmetic mean) 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 $n?$