Question

Given the sequence 12, 6, 0, −6
, . . . , identify the explicit formula that represents the sequence.(1 point)
Responses

An=12+(n−1)(−6)
upper A subscript n baseline equals 12 plus left parenthesis n minus 1 right parenthesis left parenthesis negative 6 right parenthesis

An=−6+(n−1)12
upper A subscript n baseline equals negative 6 plus left parenthesis n minus 1 right parenthesis 12

An=6(−12)n−1
upper A subscript n baseline equals 6 left parenthesis negative 12 right parenthesis superscript n minus 1 baseline

An=12(−6)n−1

Answer 1

To find the explicit formula for the sequence \(12, 6, 0, -6, \ldots\), we first observe the pattern of the sequence.

1. **Identify the first term**: The first term \(A_1\) is \(12\).
2. **Identify the common difference**: The difference between consecutive terms is:
- \(6 - 12 = -6\)
- \(0 - 6 = -6\)
- \(-6 - 0 = -6\)

The common difference \(d = -6\).

3. **Use the formula for the \(n\)-th term** of an arithmetic sequence:
\[
A_n = A_1 + (n-1)d
\]

Substituting the values we have:
- \(A_1 = 12\)
- \(d = -6\)

Therefore, the formula becomes:
\[
A_n = 12 + (n-1)(-6)
\]

This corresponds to the first option:
\[
A_n = 12 + (n-1)(-6)
\]

Thus, the correct response is:
**An=12+(n−1)(−6)**