Question

Consider the sequence 41, 29, 17, 5...

The recursive function is ________ with A1 =
____.

(1 point)
Responses

An= An−1+12, 53
An= An−1+12, 53

An= An−1−12, 41
An= An−1−12, 41

An= 12An−1, −12
An= 12An−1, −12
Question 8
30.

Answer 1

To identify the recursive function for the sequence \(41, 29, 17, 5, \ldots\), we can analyze the differences between consecutive terms.

- \(41 - 29 = 12\)
- \(29 - 17 = 12\)
- \(17 - 5 = 12\)

Each term is decreasing by \(12\) from the previous term. Thus, we can express the term \(A_n\) as a function of the previous term \(A_{n-1}\):

\[
A_n = A_{n-1} - 12
\]

To find the initial term (\(A_1\)), we look at the first term of the sequence, which is \(41\). Therefore, we can express \(A_1\) as:

\[
A_1 = 41
\]

Putting this together, the recursive function is:

\[
A_n = A_{n-1} - 12, \, A_1 = 41
\]

So the complete answer would be:

**Recursive function:** \(A_n = A_{n-1} - 12\), **with \(A_1 = 41\)** (the second response option).