Complete the Number Sequence: 800,875, 800,870, and Beyond

Arithmetic Sequences with Decimal Differences

Complete the sequence:

800,875, 800,870,  800{,}875,\ 800{,}870, \ \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:

800,875, 800,870,  800{,}875,\ 800{,}870, \ \ldots

2

Step-by-step solution

To solve this problem, follow these steps:

  • Step 1: Identify the difference between the given terms.

  • Step 2: Continue the pattern using this difference.

  • Step 3: Select the right sequence from the choices given.

Let's begin:

Step 1: Calculate the difference in the sequence.
Given the sequence: 800,875, 800,870...

The difference between 800,875 and 800,870 is
800,875800,870=5800,875 - 800,870 = 5.

This indicates that each term decreases by 5.

Step 2: Apply the same pattern to complete the sequence.

  • The next term after 800,870 is 800,8705=800,865800,870 - 5 = 800,865.

  • The term after 800,865 is 800,8655=800,860800,865 - 5 = 800,860.

  • The term after 800,860 is 800,8605=800,855800,860 - 5 = 800,855.

Therefore, the complete sequence is: 800,875, 800,870, 800,865, 800,860, 800,855800,875,\ 800,870,\ 800,865,\ 800,860,\ 800,855.

Step 3: Choose the correct sequence from the options:
The correct multiple-choice option is:

800,865, 800,860, 800,855 800{,}865,\ 800{,}860,\ 800{,}855

Thus, the sequence is completed as follows:

800,865, 800,860, 800,855 800{,}865,\ 800{,}860,\ 800{,}855

3

Final Answer

800,865, 800,860, 800,855 800{,}865,\ 800{,}860, \ 800{,}855

Key Points to Remember

Essential concepts to master this topic
  • Pattern Recognition: Find the common difference between consecutive terms
  • Technique: Calculate 800,870800,875=5 800,870 - 800,875 = -5 to find pattern
  • Check: Verify each term decreases by exactly 5: 875→870→865→860→855 ✓

Common Mistakes

Avoid these frequent errors
  • Assuming the pattern increases instead of decreases
    Don't look at 800,875 then 800,870 and think it increases = wrong direction! This happens when you subtract incorrectly or don't pay attention to which number is larger. Always calculate second term minus first term to find the true direction.

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 if the sequence is increasing or decreasing?

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Compare the first two terms! If the second term is smaller than the first (like 800,870 < 800,875), the sequence is decreasing. If it's larger, the sequence is increasing.

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

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The commas are just for easier reading! Treat 800,875 as 800875 when calculating. The difference is still 800875800870=5 800875 - 800870 = 5 , but it's decreasing by 5 each time.

Can arithmetic sequences have different common differences?

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No! In an arithmetic sequence, the difference between consecutive terms must be exactly the same throughout the entire sequence. That's what makes it 'arithmetic'.

How many terms should I find to complete the sequence?

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Look at the answer choices! They typically show 3 additional terms after the given ones. Calculate each term by subtracting the common difference from the previous term.

What if my calculated terms don't match any answer choice?

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Double-check your common difference calculation! Make sure you're subtracting in the right order: second term minus first term. Also verify you're applying the pattern consistently.

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