Question

Which is a recursive rule for the arithmetic sequence 17, 13, 9, 5...?

A (1) equals 17; f(n) equals f(n-1) minus 4
B f(1) equals 17; f(n) equals f(n-1) plus 4
C (1) equals 5; f(n) equals f(n-1) plus 4
D f(1) equals 5; f(n) equals f(n-1) minus 4

Answer 1

The recursive rule for the arithmetic sequence is f(1) = 17; f(n) = f(n-1) - 4, corresponding to option A.

Step-by-step explanation:

The question asks for the recursive rule of an arithmetic sequence. To determine which rule applies, we need to identify the pattern in the sequence. The given sequence starts with 17 and then each term decreases by 4: 17, 13, 9, 5, ...
The recursive formula for an arithmetic sequence is generally written as f(n) = f(n-1) + d, where d is the common difference between terms. In this sequence, the common difference is -4, since each term is 4 less than the previous term.

Therefore, the recursive rule is: f(1) = 17; f(n) = f(n-1) - 4, which corresponds to option A.