Final answer:
The explicit formula for the nth term of the given arithmetic sequence is B) A_n = 3n + 12, derived from the first term 15 and the common difference of 3.
Step-by-step explanation:
To find the explicit formula for the nth term (A_n) of an arithmetic sequence, we need to determine the first term (a_1) and the common difference (d). Looking at the given sequence 15, 18, 21, 24, we observe that the first term is 15 and the common difference is 3, since each term is 3 more than the previous one.
The formula for the nth term of an arithmetic sequence is A_n = a_1 + (n - 1)d. Plugging in the values we found, we get A_n = 15 + (n - 1) * 3.
Expanding this, we have A_n = 15 + 3n - 3, which simplifies to A_n = 3n + 12. Therefore, the correct option is B) A_n = 3n + 12.