Find the recursive formula for the arithmetic sequence 7, 5, 3, 1, −1

Question

, . . .(1 point)
Responses

a1=7
, an=−2an−1
a subscript 1 baseline equals 7 , a subscript n baseline equals negative 2 a subscript n minus 1 baseline

a1=7
, an=2an−1
a subscript 1 baseline equals 7 , a subscript n baseline equals 2 a subscript n minus 1 baseline

a1=7
, an=an−1+2
a subscript 1 baseline equals 7 , a subscript n baseline equals a subscript n minus 1 baseline plus 2

a1=7
, an=an−1−2

Answer 1

The given arithmetic sequence is 7, 5, 3, 1, -1, ...

To identify the recursive formula, we note the first term:

• \( a_1 = 7 \)

Next, we can determine the pattern of the sequence. The common difference between consecutive terms is:

• \( 5 - 7 = -2 \)
• \( 3 - 5 = -2 \)
• \( 1 - 3 = -2 \)
• \( -1 - 1 = -2 \)

This shows that each term is obtained by subtracting 2 from the previous term. Therefore, the recursive relation can be expressed as:

• \( a_n = a_{n-1} - 2 \)

Putting it all together, the recursive formula for the arithmetic sequence is:

• \( a_1 = 7 \)
• \( a_n = a_{n-1} - 2 \)

So, the correct response is:

a1=7, an=an−1−2