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

Question

, . . .(1 point)
Responses

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=−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

Answer 1

To find the recursive formula for the given arithmetic sequence 7, 5, 3, 1, −1, we need to observe how the sequence changes from one term to the next.

1. The first term \( a_1 \) is 7.
2. The second term \( a_2 \) is 5, which is \( 7 - 2 \).
3. The third term \( a_3 \) is 3, which is \( 5 - 2 \).
4. The fourth term \( a_4 \) is 1, which is \( 3 - 2 \).
5. The fifth term \( a_5 \) is -1, which is \( 1 - 2 \).

From this analysis, we can see that each term can be found by subtracting 2 from the previous term. Thus, we can express this in a recursive formula:

• The first term is defined as \( a_1 = 7 \).
• The subsequent terms are defined as \( a_n = a_{n-1} - 2 \).

Therefore, the correct recursive formula for this sequence is: \[ a_1 = 7, \quad a_n = a_{n-1} - 2 \quad \text{for } n > 1. \]

So, the correct response is: a1=7, an=an−1−2.