Complete the Sequence: Finding Numbers After 10,000, 9,000, 8,000

Q: How do I know if the sequence is increasing or decreasing?

Look at the given terms! Since $ 10,000 > 9,000 > 8,000 $, the numbers are getting smaller, so the sequence is decreasing.

Q: What if the pattern isn't obvious at first glance?

Calculate the difference between consecutive terms: $ 9,000 - 10,000 = -1,000 $ and $ 8,000 - 9,000 = -1,000 $. The common difference is -1,000.

Q: Can sequences have different patterns besides adding or subtracting?

Yes! Sequences can involve multiplication, division, or more complex patterns. Always check if the difference between terms is constant first - that indicates an arithmetic sequence.

Q: How do I check my answer is correct?

Verify that each term follows the pattern: $ 8,000 - 1,000 = 7,000 $, $ 7,000 - 1,000 = 6,000 $, $ 6,000 - 1,000 = 5,000 $ ✓

Arithmetic Sequences with Thousand-Unit Intervals

Complete the sequence:

$10{,}000,\ 9{,}000,\ 8{,}000, \ \ldots$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Complete the sequence:

$10{,}000,\ 9{,}000,\ 8{,}000, \ \ldots$

Step-by-step solution

To solve this problem, let's analyze the sequence:

Step 1: Observe the provided sequence: $10,000, 9000, 8000$ .
Step 2: Determine the pattern, which is a decrease of 1000 each step.
Step 3: Continue this pattern: Starting from 8000, the next term is $8000 - 1000 = 7000$ .
Step 4: Continue again: $7000 - 1000 = 6000$ .
Step 5: Continue one more time: $6000 - 1000 = 5000$ .

Thus, the completed sequence after $10,000, 9000, 8000$ becomes $7000, 6000, 5000$ .

Therefore, confirming the correct choice, the answer to the problem is $7000,6000,5000$ .

Final Answer

$7{,}000,\ 6{,}000,\ 5{,}000$

Key Points to Remember

Essential concepts to master this topic

Pattern Recognition: Identify the common difference between consecutive terms
Calculation: Subtract 1,000 from each term: 8,000 - 1,000 = 7,000
Verification: Check that each difference equals -1,000 consistently ✓

Common Mistakes

Avoid these frequent errors

Adding instead of subtracting the pattern
Don't add 1,000 to continue the sequence = 9,000, 10,000, 11,000! This reverses the decreasing pattern shown in the given terms. Always identify whether the sequence increases or decreases first, then apply the correct operation.

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

How do I know if the sequence is increasing or decreasing?

Look at the given terms! Since $10,000 > 9,000 > 8,000$ , the numbers are getting smaller, so the sequence is decreasing.

What if the pattern isn't obvious at first glance?

Calculate the difference between consecutive terms: $9,000 - 10,000 = -1,000$ and $8,000 - 9,000 = -1,000$ . The common difference is -1,000.

Can sequences have different patterns besides adding or subtracting?

Yes! Sequences can involve multiplication, division, or more complex patterns. Always check if the difference between terms is constant first - that indicates an arithmetic sequence.

What happens if I continue this sequence further?

Keep subtracting 1,000: after 5,000 comes 4,000, then 3,000, 2,000, 1,000, 0, and eventually negative numbers like -1,000, -2,000...

How do I check my answer is correct?

Verify that each term follows the pattern: $8,000 - 1,000 = 7,000$ , $7,000 - 1,000 = 6,000$ , $6,000 - 1,000 = 5,000$ ✓

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