Final answer:
The recursive rule for the given arithmetic sequence is a_n = a_{n-1} + 6 with a_1 = 62. The explicit rule is a_n = 62 + (n - 1) × 6.
Step-by-step explanation:
To complete the recursive rule and explicit rule for the arithmetic sequence 62, 68, 74, 80, 86..., we first identify the common difference between consecutive terms. This is calculated by subtracting any term from the one that follows it, which in this case, gives us 68 - 62 = 6. Therefore, the common difference is 6.
Recursive Rule
The recursive rule for an arithmetic sequence can be defined as each term is equal to the previous term plus the common difference. For our sequence, the recursive rule is:
an = an-1 + 6
with the first term a1 = 62.
Explicit Rule
The explicit rule for 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. For this sequence:
an = 62 + (n - 1) × 6