Final answer:
To create a recursive rule for the sequence f(x) = 12 + 5(x-1), identify the initial term as f(1) = 12. The recursive rule is then f(x) = f(x-1) + 5, with the first term f(1) = 12.
Step-by-step explanation:
To find the recursive rule for the given sequence f(x) = 12 + 5(x-1), we need to express f(x) in terms of the previous term f(x-1). This sequence is defined explicitly, but we can convert it into a recursive rule with a starting value and a rule for generating each term from the previous term.
Let's denote f(1) as the first term in the sequence. Since when x = 1, we have:
f(1) = 12 + 5(1-1) = 12 + 5(0) = 12
This is our starting value for the sequence, also known as the initial condition. Now we need to find the recursive relation.
For any term in the sequence f(x), the previous term would be f(x-1), and based on the given formula, we would subtract 5 from f(x) to get f(x-1). So, we get:
f(x) = f(x-1) + 5
The recursion starts at x=2 because we have the initial condition for x=1 already. Therefore, for x ≥ 2:
f(x) = f(x-1) + 5, with f(1) = 12