Final answer:
The correct nth term rule for the arithmetic sequence 8, 15, 22, 29 is (a) 7n + 1, derived from the formula for the nth term of an arithmetic sequence.
Step-by-step explanation:
The sequence given is 8, 15, 22, 29 which is an arithmetic sequence because the difference between consecutive terms is constant. This constant difference is known as the common difference, and it can be found by subtracting any term from the subsequent term. Here, the common difference is 15 - 8 = 7. The nth term of an arithmetic sequence is given by the formula an = a1 + (n - 1)d, where a1 is the first term and d is the common difference. Using the provided sequence, a1 = 8 and d = 7. Therefore, the nth term is an = 8 + (n - 1)×7 = 7n + 1. So, the correct nth term rule for the sequence is option (a) 7n + 1.