Final answer:
The nth term of an arithmetic sequence is given by the formula a_n = a_1 + (n-1)d, while the nth term of a geometric sequence is given by the formula a_n = a_1 * r^(n-1). The other two options are not standard formulas for sequences.
Step-by-step explanation:
The student's question relates to finding the nth term of a sequence. The four options given represent different types of sequences: (a) arithmetic sequence, (b) geometric sequence, (c) incorrect formula for a sequence, and (d) another incorrect formula. An arithmetic sequence follows the format a_n = a_1 + (n-1)d, where a_n is the nth term, a_1 is the first term, d is the common difference, and n is the term number.
A geometric sequence follows the format a_n = a_1 * r^(n-1), where r is the common ratio. The expression a_n = a_1 * (n-1)d does not represent a standard sequence formula, and neither does a_n = a_1 + r^(n-1), unless it's describing a sequence with a base addition and an exponential component related to the term number, which is uncommon.