Question

Find the recursive formula for the arithmetic sequence 7, 5, 3, 1, −1
, . . .(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=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=an−1+2

Answer 1

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

To find the recursive formula, we first note that the first term \( a_1 = 7 \).

To find the recursive relationship, we observe that each term is obtained by subtracting 2 from the previous term:

- \( a_2 = a_1 - 2 = 7 - 2 = 5 \)
- \( a_3 = a_2 - 2 = 5 - 2 = 3 \)
- \( a_4 = a_3 - 2 = 3 - 2 = 1 \)
- \( a_5 = a_4 - 2 = 1 - 2 = -1 \)

The pattern continues that each term is equal to the previous term minus 2.

Thus, the recursive formula is:

\[
a_1 = 7
\]
\[
a_n = a_{n-1} - 2 \quad \text{for } n \geq 2
\]

The correct option is:

**a1=7, an=an−1−2**