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=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

a1=7, an=an−1+2

Answer 1

To find the recursive formula for the given arithmetic sequence 7, 5, 3, 1, -1, ..., we can observe the pattern of the sequence.

1. Identify the first term: \( a_1 = 7 \)

2. Determine the common difference: The difference between consecutive terms is: \( 5 - 7 = -2 \)
   \( 3 - 5 = -2 \)
   \( 1 - 3 = -2 \)
   \( -1 - 1 = -2 \)

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

3. Write the recursive formula: The general form of a recursive formula for an arithmetic sequence is: \( a_n = a_{n-1} + d \) In this case, since the common difference \( d = -2 \), we have: \( a_n = a_{n-1} - 2 \)

Putting this together, the recursive formula is:

• \( a_1 = 7 \)
• \( a_n = a_{n-1} - 2 \)

Thus, the correct response is:

a1=7, an=an−1−2
\( a_1 = 7, \quad a_n = a_{n-1} - 2 \)