Question

Find the recursive formula for the arithmetic sequence 7, 5, 3, 1, −1
−
1
, . . .(1 point)
Responses

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

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

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

a1=7
𝑎
1
=
7
, an=an−1+2

Answer 1

The recursive formula for the given arithmetic sequence \( 7, 5, 3, 1, -1, \ldots \) can be defined by the first term \( a_1 = 7 \) and the common difference \( d = -2 \) (since each term decreases by 2).

Thus, the recursive formula is:

\[
a_1 = 7,
\]
\[
a_n = a_{n-1} - 2 \, \text{for } n > 1.
\]

So the correct response is:

**a1=7, an=an−1−2** (which corresponds to the first option you provided).