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=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 minus 2

a1=7, an=an−1+2

Answer 1

To find the recursive formula for the given arithmetic sequence: 7, 5, 3, 1, −1, ..., we need to identify the first term and the common difference.

1. The first term \( a_1 \) is 7.
2. The common difference \( d \) can be calculated as:
- \( 5 - 7 = -2 \)
- \( 3 - 5 = -2 \)
- \( 1 - 3 = -2 \)
- \( -1 - 1 = -2 \)

The common difference is \( -2 \).

Now we can express the recursive formula:
- The first term is \( a_1 = 7 \).
- The general recursive relation can be stated as:
\[
a_n = a_{n-1} - 2
\]
for \( n > 1 \).

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

The correct response is:
**a1=7, an=an−1−2**