Final answer:
Assuming the sequence is meant to be arithmetic and has a typo, the correct rule for the nth term of the sequence assuming a common difference of 5 is A) a_n = 5n - 4.
Step-by-step explanation:
The student has provided the sequence 1, 6, 11, and 21, and needs to find the rule for the nth term of the arithmetic sequence. Upon examination, it appears there might be a mistake as this sequence does not follow a consistent difference between its terms. However, if we were to assume that there's a typo and the sequence should be 1, 6, 11, 16, ..., which is a proper arithmetic sequence with a common difference of 5, we can find the nth term rule.
To find the nth term (an), we see that the sequence starts at 1 (which is 5*1 - 4) and increases by 5 each time. So the nth term can be described by the formula an = 5n - 4.
Thus, the correct rule for this arithmetic sequence, if it were to be consistent with a difference of 5, would be option A) an = 5n - 4.