Final answer:
Recursive rules for the given sequences are: For sequence a) an = an-1 + 5, a1 = 4; and for sequence b) an = an-1 - 5, a1 = 50.
Step-by-step explanation:
To write a recursive rule for the nth term of the given sequences, we should look at the pattern in the sequence to determine what is happening from one term to the next.
For sequence a) 4, 9, 14, 19, ...:
This is an arithmetic sequence where each term is 5 more than the previous term. So, if we call the nth term an, the recursive rule is:
an = an-1 + 5, for n ≥ 2 with the initial term a1 = 4.
For sequence b) 50, 45, 40, 35, 30, ...:
This is also an arithmetic series, but each term is 5 less than the previous term. The recursive rule is:
an = an-1 - 5, for n ≥ 2 with the initial term a1 = 50.