Final answer:
The algebraic expression that represents the nth term of the sequence in question is n², derived from manipulating the terms in a systematic way according to the instructions given.
Step-by-step explanation:
To determine which algebraic expression represents the nth number in the given sequence, we need to analyze the provided information. The information suggests a manipulation of terms that are in an arithmetic progression: 1, 3, 5, ..., (2n - 1). The process involves taking (n - 1) from the last term and adding it to the first term. Applying this to all the terms in pairs until an expression containing only 'n' remains, results in the formula 2n². Therefore, this process reveals that the algebraic expression that represents the nth term of an arithmetic sequence starting with 1 and increasing by 2 each term (odd numbers) is indeed n², not 2n + 1, n², or 3n - 2.