Given the sequence 12, 6, 0, −6

Question

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

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

Answer 1

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

The first term \( A_1 \) is 12. The second term \( A_2 \) is 6. The third term \( A_3 \) is 0. The fourth term \( A_4 \) is -6.

Next, we can notice that the sequence is decreasing by 6 each time:

• \( 12 - 6 = 6 \)
• \( 6 - 6 = 0 \)
• \( 0 - 6 = -6 \)

This indicates that the sequence is an arithmetic sequence where the first term \( a = 12 \) and the common difference \( d = -6 \).

The general formula for an arithmetic sequence is given by: \[ A_n = a + (n - 1)d \] Substituting the values we have:

• \( a = 12 \)
• \( d = -6 \) So, the formula becomes: \[ A_n = 12 + (n - 1)(-6) \] This matches the first response you have provided.

Therefore, the correct explicit formula that represents the sequence is: \[ A_n = 12 + (n - 1)(-6) \]