Determine the Rule: Continuing the Arithmetic Sequence 200,000, 210,000, ...

Q: How do I know what the common difference is?

Subtract the first term from the second term: $ 210,000 - 200,000 = 10,000 $. This common difference stays the same throughout the entire sequence.

Q: What if I calculated a different pattern by mistake?

Double-check by making sure your pattern works with all given terms. If 200,000 + your difference = 210,000, then you're on the right track!

Q: Do arithmetic sequences always add the same amount?

Yes! That's what makes them arithmetic. The difference between any two consecutive terms is always the same number.

Q: Can the common difference be negative?

Absolutely! If the sequence is decreasing (like 100, 90, 80...), the common difference would be negative (-10 in this example).

Arithmetic Sequences with Large Numbers

Complete the sequence:

$200{,}000,\ 210{,}000, \ \ldots$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Complete the sequence:

$200{,}000,\ 210{,}000, \ \ldots$

Step-by-step solution

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

Step 1: Identify the difference between the given terms.
Step 2: Use this difference to calculate subsequent terms.

Now, let's proceed with these steps:
Step 1: The given terms are 200,000 and 210,000. The difference between these terms is $210,000 - 200,000 = 10,000$ .

Step 2: Assuming this sequence follows an arithmetic pattern, the common difference is $10,000$ . Therefore, each subsequent number is the previous number plus $10,000$ .

Let's find the next few terms:

The term after 210,000 is $210,000 + 10,000 = 220,000$ .
The subsequent term is $220,000 + 10,000 = 230,000$ .
The next term is $230,000 + 10,000 = 240,000$ .

Therefore, the complete sequence is $200,000, 210,000, 220,000, 230,000, 240,000$ .

The correct answer choice is: $220,000, 230,000, 240,000$ , which matches option 3.

Final Answer

$220{,}000,\ 230{,}000, \ 240{,}000$

Key Points to Remember

Essential concepts to master this topic

Rule: Find common difference by subtracting consecutive terms
Technique: Add common difference 10,000 to each term: 210,000 + 10,000 = 220,000
Check: Verify pattern continues: 200,000, 210,000, 220,000, 230,000, 240,000 ✓

Common Mistakes

Avoid these frequent errors

Assuming the pattern continues with smaller differences
Don't assume the next term is 211,000 just because it's "one more" = wrong pattern! This ignores the actual common difference of 10,000. Always calculate the difference between given terms first.

Practice Quiz

Test your knowledge with interactive questions

Complete the sequence:

$20{,}000,\ 20{,}001,\ 20{,}002, \ \ldots$

FAQ

Everything you need to know about this question

How do I know what the common difference is?

Subtract the first term from the second term: $210,000 - 200,000 = 10,000$ . This common difference stays the same throughout the entire sequence.

What if I calculated a different pattern by mistake?

Double-check by making sure your pattern works with all given terms. If 200,000 + your difference = 210,000, then you're on the right track!

Do arithmetic sequences always add the same amount?

Yes! That's what makes them arithmetic. The difference between any two consecutive terms is always the same number.

Can the common difference be negative?

Absolutely! If the sequence is decreasing (like 100, 90, 80...), the common difference would be negative (-10 in this example).

How many terms should I find to complete the sequence?

Look at the answer choices to see how many terms they're asking for. In this problem, you need to find the next three terms after 210,000.

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