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

Question

, . . .(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 plus 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=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

Answer 1

To find the recursive formula for the given arithmetic sequence \(7, 5, 3, 1, -1, \ldots\), we first observe that each term decreases by 2 from the previous term.

The first term of the sequence is: \[ a_1 = 7 \]

The relationship between consecutive terms can be described as: \[ a_n = a_{n-1} - 2 \]

Therefore, the recursive formula for the sequence is: \[ \begin{align*} a_1 &= 7 \ a_n &= a_{n-1} - 2 \quad \text{for } n > 1 \end{align*} \]

Thus, the correct response is: \[ \text{a)} \quad a_1 = 7, \quad a_n = a_{n-1} - 2 \]