Complete the Sequence: Finding Next Terms After 5,000, 5,100, 5,200

Q: How do I know if it's really adding 100 each time?

Check the differences: 5100 - 5000 = 100 and 5200 - 5100 = 100. When the differences are equal, you have an arithmetic sequence!

Q: Could the pattern be something other than adding 100?

Always check the simplest pattern first. Since 5000 → 5100 → 5200 increases by exactly 100 each time, that's your pattern. Don't look for complex rules when simple ones work!

Q: What if I made an arithmetic mistake?

Double-check: 5200 + 100 = 5300Then: 5300 + 100 = 5400Finally: 5400 + 100 = 5500Each step should add exactly 100!

Arithmetic Sequences with Constant Differences

Complete the sequence:

$5{,}000,\ 5{,}100,\ 5{,}200, \ \ldots$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Complete the sequence:

$5{,}000,\ 5{,}100,\ 5{,}200, \ \ldots$

Step-by-step solution

To solve this problem, we need to determine the pattern in the sequence:

Step 1: Identify the pattern by finding the difference between the terms 5000 and 5100.
Step 2: Confirm that this difference is consistent between 5100 and 5200.
Step 3: Extend the sequence by the same difference to find the next three terms.

Now, let's find the solution:

Step 1: The difference between 5100 and 5000 is $5100 - 5000 = 100$ .
Step 2: Similarly, the difference between 5200 and 5100 is $5200 - 5100 = 100$ .
This confirms that the sequence is increasing by 100.

Step 3: To find the next three terms, we continue adding 100:

The term after 5200 is $5200 + 100 = 5300$ .
The next term is $5300 + 100 = 5400$ .
Finally, the next term is $5400 + 100 = 5500$ .

Therefore, the next three numbers in the sequence are $5300, 5400, 5500$ .

Final Answer

$5{,}300,\ 5{,}400,\ 5{,}500$

Key Points to Remember

Essential concepts to master this topic

Pattern Rule: Find the common difference between consecutive terms
Technique: Add the difference repeatedly: 5200 + 100 = 5300
Check: Verify each difference is the same: 100, 100, 100 ✓

Common Mistakes

Avoid these frequent errors

Assuming the pattern changes or looking for complex rules
Don't overthink simple patterns by looking for multiplication or other complex operations = wrong sequence! This leads to answers like 5,250 or 5,510. Always check if the difference between consecutive terms is the same first.

Practice Quiz

Test your knowledge with interactive questions

Complete the sequence:

$1{,}113,\ 1{,}112,\ 1{,}111, \ \ldots$

FAQ

Everything you need to know about this question

How do I know if it's really adding 100 each time?

Check the differences: 5100 - 5000 = 100 and 5200 - 5100 = 100. When the differences are equal, you have an arithmetic sequence!

What if the numbers were going down instead?

The same rule applies! If you had 5200, 5100, 5000, the common difference would be -100 (negative). Just keep subtracting 100 to continue the sequence.

Could the pattern be something other than adding 100?

Always check the simplest pattern first. Since 5000 → 5100 → 5200 increases by exactly 100 each time, that's your pattern. Don't look for complex rules when simple ones work!

How many terms should I find to complete the sequence?

The question shows three dots (...) after three given terms, so typically find the next three terms: 5300, 5400, 5500. This maintains the same pattern length.

What if I made an arithmetic mistake?

Double-check: 5200 + 100 = 5300
Then: 5300 + 100 = 5400
Finally: 5400 + 100 = 5500

Each step should add exactly 100!

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