Question

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

Answer 1

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

To find the recursive formula, we can observe the pattern in the sequence:

- The first term \( a_1 \) is 7.
- The common difference \( d \) is -2 (since each term is obtained by subtracting 2 from the previous term).

The general structure of a recursive formula for an arithmetic sequence is:
- \( a_1 \) is the first term,
- \( a_n = a_{n-1} + d \) where \( d \) is the common difference.

For this sequence:
- The first term \( a_1 = 7 \),
- The common difference \( d = -2 \).

So, the recursive formula is:
- \( a_1 = 7 \)
- \( a_n = a_{n-1} - 2 \)

Thus, the correct answer is:
**a1=7, an=an−1−2**.