Explain how to write the explicit rule for the arithmetic sequence from the given information.

Answer:

To write the explicit rule, first determine the common difference and the initial term. Given that each term is 8 more than the previous, the common difference (d) is 8. The initial term (a1) is 42. Using the general explicit formula for an arithmetic sequence, a_n = a1 + (n – 1)d, substitute 42 for a1 and 8 for d to find the rule. The resulting explicit rule for the sequence is a_n = 42 + (n – 1)8.