To describe the sequence \(-2, 4, -8\), we first observe the pattern of the terms.
- The first term (when \(n = 1\)) is \(-2\).
- The second term (when \(n = 2\)) is \(4\).
- The third term (when \(n = 3\)) is \(-8\).
Next, let's examine the pattern in the terms:
- The first term is \(-2\) (which is \(-2 \times 1\)).
- The second term is \(4\) (which is \(-2 \times -2\)).
- The third term is \(-8\) (which is \(-2 \times 4\)).
There is a clear trend where each term alternates in sign, and each term can be represented by multiplying the previous term by \(-2\).
We can express the \(n\)-th term of the sequence as: \[ a_n = -2 \times (-2)^{n-1} \] Thus, putting it in the desired format: \[ a_n = -2 \cdot (-2)^{n-1} \]
So, the completed equation to describe the sequence is: \[ a_n = -2 \cdot (-2)^{n-1} \]