Formulas for Sequences Quick Check

Question

4 of 54 of 5 Items
Question
Find the recursive formula for the arithmetic sequence 7, 5, 3, 1, −1
, . . .(1 point)
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=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

Answer 1

To find the recursive formula for the arithmetic sequence 7, 5, 3, 1, −1, we need to identify two components:

1. The first term of the sequence.
2. The common difference between successive terms.

The first term \( a_1 \) is 7.

To find the common difference \( d \), we can subtract the second term from the first term:

\[ d = 5 - 7 = -2 \]

Now, we can write the recursive formula.

The recursive formula format is:

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

Since our common difference is -2, we have:

• \( a_n = a_{n-1} - 2 \)

Therefore, the correct answer from the options provided is:

a1=7, an=an−1−2

So, the complete recursive formula is:

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