To identify the correct recursive equation for the arithmetic sequence 6, 2, −2, −6, ..., we need to analyze the pattern in the sequence.
The first term \( a_1 \) is 6. The difference between consecutive terms is:
- \( 2 - 6 = -4 \)
- \( -2 - 2 = -4 \)
- \( -6 - (-2) = -4 \)
The sequence decreases by 4 with each term. This indicates that the recursive formula should reflect that relationship.
Thus, we can summarize this as:
- The first term is \( a_1 = 6 \)
- The subsequent terms are defined by subtracting 4 from the previous term: \( a_n = a_{n-1} - 4 \)
Looking at the given options, we see that:
Option #2:
- \( a_1 = 6 \)
- \( a_n = a_{n-1} - 4 \)
This matches the defined terms of our sequence.
Therefore, the correct option is:
Option #2.