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

Question

Responses

An=12(−6)n−1

An=−6+(n−1)12

An=12+(n−1)(−6)

An=6(−12)n−1

Answer 1

To find the explicit formula for the sequence \(12, 6, 0, -6, \ldots\), let's first look at how the sequence changes.

The sequence starts at 12 and decreases by 6 each time:

• From 12 to 6, it decreases by \(6\).
• From 6 to 0, it decreases by \(6\).
• From 0 to -6, it decreases by \(6\).

This means it is an arithmetic sequence where:

• The first term \(A_1 = 12\),
• The common difference \(d = -6\).

The explicit formula for an arithmetic sequence can be expressed as:

\[ A_n = A_1 + (n-1)d \]

Substituting in our values:

\[ A_n = 12 + (n-1)(-6) \]

This corresponds to the option:

An=12+(n−1)(−6)

Thus, the correct answer is:

An=12+(n−1)(−6).