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 plus 2

a1=7, an=an−1−2

Answer 1

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

To find the recursive formula, we first identify the first term and the common difference.

• The first term \( a_1 = 7 \).
• The common difference \( d \) can be found by subtracting any term from the next term:
  • \( 5 - 7 = -2 \)
  • \( 3 - 5 = -2 \)
  • \( 1 - 3 = -2 \)
  • \( -1 - 1 = -2 \)

Thus, the common difference \( d = -2 \).

The recursive formula for an arithmetic sequence is generally expressed as:

\[ a_1 = \text{first term}, \quad a_n = a_{n-1} + d \]

In this case, we can set the recursive formula as follows:

\[ a_1 = 7, \quad a_n = a_{n-1} - 2 \]

Therefore, the correct response is:

a1=7, an=an−1−2