Complete the Sequence: Find the Next Number Following 955, 1000, 1005

Q: How do I know which difference to use?

Look for the most recent consistent pattern. Here, both 1000 to 1005 and the continuing pattern show a difference of 5, so that's your common difference.

Q: Can I just guess from the answer choices?

While answer choices can help verify your work, always solve systematically first. Understanding the pattern helps you solve similar problems even without multiple choice options!

Arithmetic Sequences with Variable Differences

Complete the sequence:

$995,\ 1{,}000,\ 1{,}005, \ \ldots$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Complete the sequence:

$995,\ 1{,}000,\ 1{,}005, \ \ldots$

Step-by-step solution

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 $1010, 1015, 1020$ .

Final Answer

$1{,}010,\ 1{,}015,\ 1{,}020$

Key Points to Remember

Essential concepts to master this topic

Pattern Recognition: Find differences between consecutive terms to identify the sequence pattern
Technique: Calculate 1000 - 995 = 5, then 1005 - 1000 = 5
Check: Verify pattern continues: 1010, 1015, 1020 each differ by 5 ✓

Common Mistakes

Avoid these frequent errors

Assuming the first large jump continues
Don't think the sequence keeps adding 45 because 1000 - 955 = 45! This ignores the second difference of 5. The large jump from 955 to 1000 appears to be a correction, and the actual pattern is adding 5. Always check at least two consecutive differences to identify the true pattern.

Practice Quiz

Test your knowledge with interactive questions

Complete the sequence:

$1{,}007,\ 1{,}008,\ 1{,}009, \ \ldots$

FAQ

Everything you need to know about this question

Why is the first difference so much bigger than the others?

The jump from 955 to 1000 (difference of 45) seems unusual, but in some sequences, there can be initial corrections or the pattern starts after a certain point. Focus on the consistent pattern you see in recent terms.

How do I know which difference to use?

Look for the most recent consistent pattern. Here, both 1000 to 1005 and the continuing pattern show a difference of 5, so that's your common difference.

What if the differences keep changing?

If differences aren't constant, look for patterns in the differences themselves! Sometimes sequences have second-order patterns where the differences form their own sequence.

Can I just guess from the answer choices?

While answer choices can help verify your work, always solve systematically first. Understanding the pattern helps you solve similar problems even without multiple choice options!

What if I get confused by the comma formatting in numbers?

The commas in numbers like 1,000 and 1,005 are just for readability. Focus on the actual values: 1000, 1005, 1010, etc. The mathematical relationships remain the same.

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