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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

1 answer

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)