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

Question

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