Analyzing the Power Pattern: Is there a Property in 256, 64, 16, 4, 1?

To identify the property of the sequence $256, 64, 16, 4, 1$, we'll calculate the ratio between each consecutive pair of terms:

• First, calculate the ratio of the second term to the first term: $\frac{64}{256} = \frac{1}{4}$.
• Next, calculate the ratio of the third term to the second term: $\frac{16}{64} = \frac{1}{4}$.
• Then, calculate the ratio of the fourth term to the third term: $\frac{4}{16} = \frac{1}{4}$.
• Finally, calculate the ratio of the fifth term to the fourth term: $\frac{1}{4} = \frac{1}{4}$.

All calculated ratios are equal to $\frac{1}{4}$. This confirms that each term in the sequence is obtained by multiplying the previous term by $\frac{1}{4}$ or equivalently, multiplying by 0.25.

Therefore, the sequence follows the property of being a geometric sequence with a common ratio of $0.25$.

This corresponds to the answer choice: $\times 0.25$ (Choice 4).