Complete the Sequence: Finding the Pattern in 480,280, 480,290, ...

Q: What if the numbers are really big like 480,000?

Big numbers work the same way! Focus on the difference between terms, not the size. The pattern $ 480{,}280 \rightarrow 480{,}290 $ shows a difference of 10, regardless of how large the numbers are.

Q: What if I get confused by the commas in large numbers?

Commas just make numbers easier to read! $ 480{,}280 $ is the same as 480280. Focus on the mathematical operation, not the formatting.

Q: How do I check if my sequence is correct?

Verify that each consecutive pair has the same difference. Check: 480,300 - 480,290 = 10, and 480,310 - 480,300 = 10 ✓

Q: Could this sequence follow a different pattern besides addition?

Always start with the simplest pattern first - addition or subtraction. Since 480,290 - 480,280 = 10, this is clearly an arithmetic sequence with constant addition.

Arithmetic Sequences with Large Number Patterns

Complete the sequence:

$480{,}280,\ 480{,}290, \ \ldots$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Complete the sequence:

$480{,}280,\ 480{,}290, \ \ldots$

Step-by-step solution

Let's proceed step-by-step to find the pattern in the sequence:

Step 1: Identify the sequence
The sequence begins with $480{,}280$ and $480{,}290$ .
Step 2: Determine the common difference
Subtract the first term from the second term: $480{,}290 - 480{,}280 = 10$ . The common difference is $10$ .
Step 3: Apply the common difference to find the next terms
- Add $10$ to the second term: $480{,}290 + 10 = 480{,}300$ .
- Add $10$ to get the next term: $480{,}300 + 10 = 480{,}310$ .
- Add $10$ again: $480{,}310 + 10 = 480{,}320$ .

Therefore, the next terms in the sequence are $480{,}300,\ 480{,}310,\ 480{,}320$ .

This matches choice 4, given the specified answer options.

Thus, we conclude that the sequence continues with $\textbf{480,300,\ 480,310,\ 480,320}$ .

Final Answer

$480{,}300,\ 480{,}310,\ 480{,}320$

Key Points to Remember

Essential concepts to master this topic

Pattern Recognition: Find the common difference by subtracting consecutive terms
Technique: Add common difference repeatedly: 480,290 + 10 = 480,300
Check: Verify each term increases by same amount: 480,300 + 10 = 480,310 ✓

Common Mistakes

Avoid these frequent errors

Assuming the pattern is addition by 1 or multiplication
Don't assume sequences always increase by 1 or multiply = wrong pattern identification! This leads to answers like 480,291 or 481,000. Always calculate the exact 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 find the common difference in a sequence?

Subtract the first term from the second term. In this case: $480{,}290 - 480{,}280 = 10$ . This common difference tells you how much to add each time.

What if the numbers are really big like 480,000?

Big numbers work the same way! Focus on the difference between terms, not the size. The pattern $480{,}280 \rightarrow 480{,}290$ shows a difference of 10, regardless of how large the numbers are.

How many terms should I find to complete the sequence?

Look at the answer choices to see how many terms are needed. In this problem, you need three more terms after the given two terms.

What if I get confused by the commas in large numbers?

Commas just make numbers easier to read! $480{,}280$ is the same as 480280. Focus on the mathematical operation, not the formatting.

How do I check if my sequence is correct?

Verify that each consecutive pair has the same difference. Check: 480,300 - 480,290 = 10, and 480,310 - 480,300 = 10 ✓

Could this sequence follow a different pattern besides addition?

Always start with the simplest pattern first - addition or subtraction. Since 480,290 - 480,280 = 10, this is clearly an arithmetic sequence with constant addition.

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