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

Question

0An =-6 + (n - 1) 12
0 An = 6(-12)"-1
O An = 12 + (n - 1) (-6)
0 An = 12(-6)"-1

Answer 1

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

1. The first term \( A(1) = 12 \)
2. The second term \( A(2) = 6 \)
3. The third term \( A(3) = 0 \)
4. The fourth term \( A(4) = -6 \)

The difference between consecutive terms is \( -6 \):

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

This indicates that the sequence decreases by 6 with each step.

The general form of a linear sequence can be written as: \[ A(n) = A(1) + (n - 1)d \] where \( A(1) \) is the first term and \( d \) is the common difference.

Here:

• \( A(1) = 12 \)
• \( d = -6 \)

Substituting the values in, we get: \[ A(n) = 12 + (n - 1)(-6) \]

This simplifies to: \[ A(n) = 12 - 6(n - 1) \] \[ A(n) = 12 - 6n + 6 \] \[ A(n) = 18 - 6n \]

From the options given, we notice the closest match is:

• \( A_n = 12 + (n - 1)(-6) \)

Thus, the explicit formula that represents the sequence is: \[ \boxed{A_n = 12 + (n - 1)(-6)} \]