Determine the Next Numbers: Completing 100,000, 200,000, ...

Q: How do I know what number to add each time?

Subtract the first term from the second term to find the common difference. In this case: $ 200{,}000 - 100{,}000 = 100{,}000 $. This is the amount you add to get each next term!

Q: What if I get confused with all the zeros?

Write out the numbers carefully or use place value thinking. $ 100{,}000 $ is "one hundred thousand" and $ 200{,}000 $ is "two hundred thousand."

Arithmetic Sequences with Large Number Patterns

Complete the sequence:

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

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Complete the sequence:

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

Step-by-step solution

To solve this problem, we need to extend the given sequence $100,000, 200,000, \ldots$ .

First, we observe the given numbers:

The first term of the sequence is $100,000$ .
The second term of the sequence is $200,000$ .

Next, we find the common difference ( $d$ ) between consecutive terms:

$d = 200,000 - 100,000 = 100,000$ .

This tells us that each term increases by $100,000$ .

Using the pattern established, we can find the next terms in the sequence:

The third term: $200,000 + 100,000 = 300,000$ .
The fourth term: $300,000 + 100,000 = 400,000$ .
The fifth term: $400,000 + 100,000 = 500,000$ .

Therefore, the next terms in the sequence are $300,000, 400,000, 500,000$ .

Given the choices, the correct sequence that matches this pattern is choice 3.

Therefore, the solution to the problem is $300,000, 400,000, 500,000$ .

Final Answer

$300{,}000,\ 400{,}000, \ 500{,}000$

Key Points to Remember

Essential concepts to master this topic

Pattern Recognition: Find the common difference between consecutive terms
Calculate: $200{,}000 - 100{,}000 = 100{,}000$ difference per term
Verify: Each term should increase by exactly $100{,}000$ ✓

Common Mistakes

Avoid these frequent errors

Adding wrong amounts or random numbers
Don't add random amounts like 1, 10, or 10,000 to continue the pattern = completely wrong sequence! This ignores the established pattern. Always find the exact difference between given terms first, then add that same amount consistently.

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 number to add each time?

Subtract the first term from the second term to find the common difference. In this case: $200{,}000 - 100{,}000 = 100{,}000$ . This is the amount you add to get each next term!

What if the numbers are really big like these?

Don't let big numbers intimidate you! The process is exactly the same as with small numbers. Focus on the pattern and difference between terms, not the size of the numbers.

Could the pattern be something other than adding?

Yes! Sequences can multiply, divide, or follow other patterns. But when you see equal differences like $100{,}000$ between terms, it's an arithmetic sequence (adding pattern).

How many terms should I find?

Look at the answer choices to see how many terms they want. Usually it's the next 3 terms after the given ones, but always check what the question is asking for!

What if I get confused with all the zeros?

Write out the numbers carefully or use place value thinking. $100{,}000$ is "one hundred thousand" and $200{,}000$ is "two hundred thousand."

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