Complete the Sequence: Finding Numbers After 1007, 1008, 1009

Arithmetic Sequences with Consecutive Integers

Complete the sequence:

1,007, 1,008, 1,009,  1{,}007,\ 1{,}008,\ 1{,}009, \ \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:

1,007, 1,008, 1,009,  1{,}007,\ 1{,}008,\ 1{,}009, \ \ldots

2

Step-by-step solution

To solve this problem, we'll identify the pattern in the sequence:

  • Step 1: Identify the order and pattern of the sequence
  • Step 2: Follow the arithmetic pattern of adding the same number to the last term to find the next numbers
  • Step 3: List the next terms in the sequence

Now, let's work through each step:

Step 1: The sequence given is 1007, 1008, 1009. We observe that each number is 1 more than the previous one.
Step 2: Continuing this pattern, the next number after 1009 is 1009+1=1010 1009 + 1 = 1010 .
Step 3: Similarly, we calculate the next numbers: 1010+1=1011 1010 + 1 = 1011 and 1011+1=1012 1011 + 1 = 1012 .

Therefore, the sequence can be completed as: 1010,1011,1012 1010, 1011, 1012 .

3

Final Answer

1,010, 1,011, 1,012 1{,}010,\ 1{,}011,\ 1{,}012

Key Points to Remember

Essential concepts to master this topic
  • Pattern: Each term increases by the same constant difference
  • Technique: Add common difference to last term: 1009+1=1010 1009 + 1 = 1010
  • Check: Verify each term differs by 1: 10101009=1 1010 - 1009 = 1

Common Mistakes

Avoid these frequent errors
  • Adding wrong increments or skipping numbers
    Don't add random amounts like 2 or 10, or jump to numbers like 1011 first = wrong sequence! This breaks the consistent pattern. Always identify the common difference first, then add it to each successive term.

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 what number to add each time?

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Look at the difference between consecutive terms! In this sequence: 10081007=1 1008 - 1007 = 1 and 10091008=1 1009 - 1008 = 1 . The pattern is adding 1 each time.

What if the sequence was going backwards?

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If numbers were decreasing (like 1009, 1008, 1007), you'd subtract the common difference instead. Always check if the sequence goes up or down!

Can I just count up from 1009?

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Yes! Since we're adding 1 each time, counting up works perfectly: 1009 → 1010 → 1011 → 1012. This is the easiest method for sequences that increase by 1.

What if I accidentally wrote 1011, 1012, 1013?

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You skipped 1010! Remember to find the very next term after 1009, which is 1010. Then continue the pattern from there.

How many terms should I find for 'complete the sequence'?

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Usually 3 terms like in this problem, but always check the answer choices! They'll show you exactly how many terms you need to find.

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