Which option is the correct recursive equation for the arithmetic sequence 6, 2, −2

Question

, −6
, . . .?

Option #1: a1=6
, an=an−1+4


Option #2: a1=6
, an=an−1−4


Option #3: a1=6
, an=4an−1


Option #4: a1=6
, an=−4an−1


(1 point)
Option #
is the correct recursive formula for the sequence.

Answer 1

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.