2025 AMC 10A Problem 5

Group the sequence into blocks. Block $k$ reads $k, k-1, \ldots, 2, 1, 2, \ldots, k-1, k,$ which is $2k - 1$ terms and ends on $k.$ So after block $k$ we’ve used $1 + 3 + \cdots + (2k-1) = k^2$ terms. Notice $2025 = 45^2.$ That’s exactly the end of block $45,$ whose last term is $45.$ Thus, E is the correct answer.