Final answer:
The recursive rule for the given sequence is an = an-1 + 6 and the explicit rule is an = -1 + 6n.
Step-by-step explanation:
The given sequence is 5, 11, 17, 23, 29. To find the recursive rule, we need to find the pattern between consecutive terms. We observe that each term is obtained by adding 6 to the previous term: 5 + 6 = 11, 11 + 6 = 17, and so on.
Therefore, the recursive rule is:
an = an-1 + 6
To find the explicit rule, we can examine the general pattern. Notice that we are adding 6 to each term, which means the common difference is 6. The first term is 5, which implies the constant term is -1 (since 5 - 6 = -1). Therefore, the explicit rule is:
an = -1 + 6n