Complete the Sequence: Finding the Next Terms in 380,000, 370,000, ...

Arithmetic Sequences with Large Number Differences

Complete the sequence:

380,000, 370,000,  380{,}000,\ 370{,}000, \ \ldots

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Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Complete the sequence:

380,000, 370,000,  380{,}000,\ 370{,}000, \ \ldots

2

Step-by-step solution

To solve this problem, we'll determine the pattern in the sequence and extend it:

  • Step 1: Identify the pattern in the sequence
  • Step 2: Calculate the common difference
  • Step 3: Use the common difference to extend the sequence

Now, let's work through each step:
Step 1: The sequence starts with 380,000 380{,}000 and 370,000 370{,}000 . By observation, the numbers are decreasing.
Step 2: Calculate the common difference: 370,000380,000=10,000 370{,}000 - 380{,}000 = -10{,}000 . This tells us the sequence decreases by 10,000 10{,}000 for each step.
Step 3: Continue the sequence using the common difference:

  • The next term after 370,000 370{,}000 is 370,00010,000=360,000 370{,}000 - 10{,}000 = 360{,}000 .
  • The following term is 360,00010,000=350,000 360{,}000 - 10{,}000 = 350{,}000 .
  • The term after that is 350,00010,000=340,000 350{,}000 - 10{,}000 = 340{,}000 .

Therefore, the completed sequence is: 360,000, 350,000, 340,000 360{,}000,\ 350{,}000, \ 340{,}000 .

3

Final Answer

360,000, 350,000, 340,000 360{,}000,\ 350{,}000, \ 340{,}000

Key Points to Remember

Essential concepts to master this topic
  • Pattern Recognition: Find the common difference between consecutive terms first
  • Technique: Subtract previous from next: 370,000380,000=10,000 370{,}000 - 380{,}000 = -10{,}000
  • Check: Verify each term follows the pattern: 360,00010,000=350,000 360{,}000 - 10{,}000 = 350{,}000

Common Mistakes

Avoid these frequent errors
  • Assuming the pattern without calculating the difference
    Don't guess that numbers decrease by 1,000 or 5,000 without checking = wrong sequence! Visual patterns can be deceiving with large numbers. Always calculate the exact difference: 370,000 - 380,000 = -10,000.

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 this is an arithmetic sequence?

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An arithmetic sequence has the same difference between consecutive terms. Since 370,000380,000=10,000 370{,}000 - 380{,}000 = -10{,}000 , we subtract 10,000 each time.

Why is the common difference negative?

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The common difference is negative because the sequence is decreasing. We go from 380,000 down to 370,000, so we subtract 10,000 each step.

What if I made a calculation error?

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Double-check by working backwards! If 360,000 is correct, then 360,000+10,000=370,000 360{,}000 + 10{,}000 = 370{,}000 should match the given term.

Can arithmetic sequences have different patterns?

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Yes! The common difference can be positive (increasing), negative (decreasing), or even fractions. The key is that it stays constant throughout the sequence.

How many terms should I find?

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The question asks for the next three terms after the given pattern. Always read carefully to see exactly how many terms are needed!

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