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 minus 2

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=2an−1

Answer 1

To find the recursive formula for the given arithmetic sequence 7, 5, 3, 1, -1, we first note the following:

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

The common difference \( d \) is -2.

Now, we can write the recursive formula for the sequence. The first term is given by \( a_1 = 7 \), and each subsequent term is found by taking the previous term and subtracting 2.

Thus, the correct recursive formula is:

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

So, the answer is:

a1=7, an=an−1−2