AMC 10B/12B 2025 (Problem 17/14)

Consider a decreasing sequence of

n

positive integers

x_1>x_2>\cdots>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

\text{(A)}\;1013

\text{(B)}\;1014

\text{(C)}\;1016

\text{(D)}\;2016

\text{(E)}\;2025