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.

To solve this problem, we will identify the progression pattern in the given sequence of numbers:

• Step 1: Examine the initial terms of the sequence 3,000, 3,010, 3,020.

Observe the difference between these terms:

• $3,010 - 3,000 = 10$
• $3,020 - 3,010 = 10$

The difference between consecutive terms is consistently 10. This indicates that the sequence increases by 10 with each new term.

Since the sequence is arithmetic and each term increases by 10, let's calculate the next few terms by adding 10 to the last given number, $3,020$:

• Next term: $3,020 + 10 = 3,030$
• Following term: $3,030 + 10 = 3,040$
• Final term required: $3,040 + 10 = 3,050$

Thus, the next three numbers in the sequence are $3,030$, $3,040$, and $3,050$.

The choice that matches this sequence completion is option 2: $3,030,\ 3,040,\ 3,050$.