Sequences / Skips up to 10,000: Increases of fifths/tens

To solve this problem, let's follow these steps:

• Step 1: Calculate the differences between consecutive terms of the sequence.
• Step 2: Use the common difference to find the next terms.
• Step 3: Verify the result with the provided answer choices.

Step 1: Calculate the differences:
The difference between the first and second terms is $1000 - 955 = 45$.
The difference between the second and third terms is $1005 - 1000 = 5$.

Step 2: Identifying that the sequence alternates increases, first by 45 and then by 5, we predict it continues by adding 5. Thus, extending the sequence, the next terms would be:
$1005 + 5 = 1010$,
$1010 + 5 = 1015$,
$1015 + 5 = 1020$.

Therefore, the next terms in the sequence are $1010, 1015, 1020$.

Step 3: Verify against provided answer choices. The correct choice is:

$1010,1015,1020$

The next numbers in the sequence are $1010, 1015, 1020$.

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.