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

Question

, . . .(1 point)
Responses

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

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

a1=7
, an=an−1+2

Answer 1

To find the recursive formula for the given arithmetic sequence \(7, 5, 3, 1, -1, \ldots\), we can observe the nature of the sequence:

1. The first term \(a_1 = 7\).
2. Each subsequent term is obtained by subtracting 2 from the previous term.

So, we can express this relationship recursively as:

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

Thus, the correct response is:

a1 = 7, an = an−1 − 2 (which corresponds to your first option).