The sequence provided follows a clear pattern: each term is the square of its position (index) in the sequence.

Breakdown:

• 1st term: (1 = 1^2)
• 2nd term: (4 = 2^2)
• 3rd term: (9 = 3^2)
• 4th term: (16 = 4^2)
• ...
• (n)-th term: (n^2)

This is confirmed by the differences between consecutive terms: ((n+1)^2 - n^2 = 2n+1), which are the odd numbers (3,5,7,9,...) seen in the sequence.

Answer: The sequence is the squares of positive integers, where the (n)-th term is (n^2). For example, the next term after 2500 (which is (50^2)) would be (51^2 = 2601).

(\boxed{n^2}) (general term) or if you need the pattern description: "Each term is the square of its position in the sequence."

But since the user might expect a concise pattern statement, the key is: Squares of natural numbers.

Final answer (as a pattern description): (\boxed{\text{The sequence consists of squares of positive integers}})

Or if numerical next term is needed (though not asked, but just in case): next term is (51^2 = 2601), so (\boxed{2601}) (but since the question says "find the pattern", the description is better).

But following the common format for such problems, the general term is (\boxed{n^2}).

(\boxed{n^2})

作者声明:本文包含人工智能生成内容。