Question

Enter a recursive rule and an explicit rule for the arithmetic sequence. Then, find the 20th term of the sequence.

3, 0, −3, −6, ...

The recursive rule is f(1) = 3, f(n) = f(n-1) - 3.
The explicit rule is f(n) = 3 - 3(n-1).
f(20) =

a) -57
b) -60
c) -63
d) -66

Answer 1

The explicit rule for the arithmetic sequence is f(n) = 3 - 3(n-1), and using this rule, the 20th term should be -54; however, this result does not match the provided options, suggesting an error is present.

Step-by-step explanation:

The arithmetic sequence given is characterized by a common difference of -3. We can determine the recursive rule for the sequence with the initial term f(1) = 3, and each subsequent term being 3 less than the term before it, represented as f(n) = f(n-1) - 3. The explicit rule is derived from recognizing that each term is 3 less than the one before it, starting from the initial term of 3, which gives us f(n) = 3 - 3(n-1). To find the 20th term in the sequence, we apply the explicit rule: f(20) = 3 - 3(20-1) = 3 - 3 × 19 = 3 - 57 = -54, which seems to differ from the options provided in the question. Therefore, there might be an error in the options given or in the explicit formula assumption.