Complete the Sequence: Finding the Pattern in 4,580, 4,570, 4,560,...

To solve this problem, we'll follow these steps:

• Step 1: Identify the difference between each given term in the sequence.
• Step 2: Confirm this difference is consistent across the initial sequence.
• Step 3: Use this pattern to determine the next terms.

Now, let's work through each step:

Step 1: Calculate the difference between the first two terms: $4580 - 4570 = 10$.

Step 2: Confirm the difference between the next terms is the same: $4570 - 4560 = 10$. This confirms a constant decrement of 10.

Step 3: Continue the sequence using this pattern:

• The next term is $4560 - 10 = 4550$.
• The following term is $4550 - 10 = 4540$.
• The final term in this sequence is $4540 - 10 = 4530$.

The next three terms in the sequence are $4550, 4540, 4530$.

Therefore, the correct answer according to the provided choices is: $4550, 4540, 4530$, which corresponds to choice 4.