To solve the question based on the image, we can analyze the sequence given and compare it with the options.

The sequence given in the problem is: $64, -16, 4, -1, \dots$.

Step 1: Analyze the sequence

1. Start with $64$ (the first term).
2. The second term is $-16$, which is $64 \times -\frac{1}{4}$.
3. The third term is $4$, which is $-16 \times -\frac{1}{4}$.
4. The fourth term is $-1$, which is $4 \times -\frac{1}{4}$.

The pattern suggests this is a geometric sequence where each term is multiplied by $-\frac{1}{4}$.

Step 2: General expression for the $n$-th term

The general formula for a geometric sequence is: $a_n = a_1 \cdot r^{n-1}$ Where:

• $a_1$ is the first term ($64$),
• $r$ is the common ratio ($-\frac{1}{4}$).

Thus: $a_n = 64 \cdot \left(-\frac{1}{4}\right)^{n-1}$

Step 3: Compare with given options

From the options:

• $256 \cdot (-0.25)^n$ does not fit because the first term would not be $64$.
• $-256 \cdot 0.25^n$ does not match the sign pattern of the sequence.
• $64 \cdot (-0.25)^n$ does not fit because it would make the first term $64 \cdot (-0.25)^1 = -16$, which is incorrect.
• $-64 \cdot 0.25^n$ does not work either.

The correct form must align with the above pattern of $64 \cdot (-0.25)^{n-1}$. However, this detail might require specific inspection for precision. If there's more clarity text refirm simpl!