Complete the Number Sequence: 20,000, 20,001, 20,002...

Arithmetic Sequences with Consecutive Integers

Complete the sequence:

20,000, 20,001, 20,002,  20{,}000,\ 20{,}001,\ 20{,}002, \ \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:

20,000, 20,001, 20,002,  20{,}000,\ 20{,}001,\ 20{,}002, \ \ldots

2

Step-by-step solution

To solve this problem, we will continue the sequence 20,000,20,001,20,002, 20,000, 20,001, 20,002, \ldots by adding 1 to the last number provided.

  • Start with the last number in the sequence, which is 20,002 20,002 .
  • Step 1: Add 1 to 20,002 20,002 to get 20,003 20,003 .
  • Step 2: Add 1 to 20,003 20,003 to get 20,004 20,004 .
  • Step 3: Add 1 to 20,004 20,004 to get 20,005 20,005 .

Thus, the continuation of the sequence is 20,003,20,004,20,005 20,003, 20,004, 20,005 .

Therefore, the correct answer is choice 1: 20,003,20,004,20,005 20,003,20,004,20,005 .

3

Final Answer

20,003, 20,004, 20,005 20{,}003,\ 20{,}004,\ 20{,}005

Key Points to Remember

Essential concepts to master this topic
  • Pattern: Each term increases by exactly 1 in this sequence
  • Technique: Add 1 to 20,002 to get 20,003, then 20,004, 20,005
  • Check: Verify difference between consecutive terms is always 1 ✓

Common Mistakes

Avoid these frequent errors
  • Adding the wrong increment amount
    Don't add 2 or 3 to continue the sequence = skipping numbers! This happens when students don't carefully observe the pattern. Always identify the exact difference between consecutive 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 identify the pattern in a number sequence?

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Look at the difference between consecutive terms. In this sequence: 20,001 - 20,000 = 1, and 20,002 - 20,001 = 1. The pattern is add 1 each time!

What if the numbers were much larger or smaller?

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The method stays the same! Whether it's 5, 6, 7 or 50,000, 50,001, 50,002, you still find the difference and continue the pattern.

Can arithmetic sequences go backwards?

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Yes! If you see 100, 99, 98, the pattern is subtract 1 each time. The difference is -1, so you'd continue with 97, 96, 95.

What if I can't see the pattern right away?

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Write out the differences! For any sequence a, b, c, calculate b - a and c - b. If they're the same, that's your pattern.

How many terms should I continue the sequence?

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The problem will tell you! Here we needed three more terms after 20,002, so we found 20,003, 20,004, and 20,005.

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