Final answer:
To find the formula for a sequence summing to n², we can demonstrate that by pairing terms to sum to 2n and reorganizing them, the formula aₙ = n² describes the sequence correctly.
Step-by-step explanation:
To determine which formula describes a given sequence, we can analyze the pattern of the sequence provided and compare it to the formulas presented. If we look at the sequence that matches the numeric pattern of the sum of squares, for instance, n terms resulting in the value n², there is an insightful approach:
Consider a series that sums to n²; this can be visualized by rearranging the terms such that pairs of them sum to 2n. For example:
Given a sequence of odd numbers 1, 3, ..., (2n - 3), (2n - 1), we take (n - 1) from the last term and add it to the first term, which yields:
2[1 + (n - 1) + 3 + ... + (2n - 3) + (2n - 1) - (n - 1)] = 2[n + 3 + ... + (2n - 3) + n].
This simplifies to 2 * n² when we take (n - 3) from the penultimate term and add it to the second term, resulting in:
2[n + n + … + n + n] = 2n².
Thus, the correct formula to describe the sequence that sums to n² is aₙ = n² (option c).