Complete the Sequence: Finding Numbers After 107, 108, 109

Arithmetic Sequences with Integer Progression

Complete the sequence:

107,108,109, 107,108,109,\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:

107,108,109, 107,108,109,\ldots

2

Step-by-step solution

To solve this problem, we'll identify that we are dealing with an arithmetic sequence where each term increases by 1.

  • Step 1: Identify the pattern in the sequence.
  • Step 2: Note that the difference between consecutive terms is 1.
  • Step 3: Extend the sequence from the last given term.

Now, let's work through these steps:

Step 1: The sequence starts at 107,108,109 107, 108, 109 . The difference is clearly 1, as each number is 1 more than its predecessor.

Step 2: The rule for this sequence is to take the last number and add 1 to generate the next number. We continue the pattern.

Step 3: Continuing from 109:

  • 109 + 1 = 110
  • 110 + 1 = 111
  • 111 + 1 = 112
  • 112 + 1 = 113

Therefore, the next numbers in the sequence are 110,111,112,113 110, 111, 112, 113 .

Hence, the correct answer choice is the one with the sequence 110,111,112,113 110, 111, 112, 113 .

3

Final Answer

110,111,112,113 110,111,112,113

Key Points to Remember

Essential concepts to master this topic
  • Pattern: Each term increases by constant difference of 1
  • Technique: Add 1 to previous term: 109 + 1 = 110
  • Check: Verify differences are equal: 110-109 = 109-108 = 108-107 = 1 ✓

Common Mistakes

Avoid these frequent errors
  • Assuming complex patterns when sequence is simple
    Don't look for complicated patterns like doubling or skipping numbers when given 107, 108, 109 = confusing answers! The simplest pattern is usually correct. Always check the difference between consecutive terms first.

Practice Quiz

Test your knowledge with interactive questions

Complete the following sequence:

\( 1,3.\ldots \)

FAQ

Everything you need to know about this question

How do I know this is an arithmetic sequence?

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Look at the differences between consecutive terms: 108 - 107 = 1, and 109 - 108 = 1. When the difference is constant, it's an arithmetic sequence!

What if the numbers were going backwards?

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If you saw 109, 108, 107, the common difference would be -1 (negative). You'd continue subtracting 1 to get 106, 105, 104, etc.

Could there be a different pattern I'm missing?

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While other patterns are possible, always start with the simplest explanation. Since 107, 108, 109 increases by 1 each time, continuing with +1 is most logical.

How many terms should I find?

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The question asks you to complete the sequence, so look at the answer choices to see how many terms they expect. Usually it's 3-4 more terms.

What if I calculated wrong?

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  • Double-check your addition: 109 + 1 = 110
  • Verify the pattern continues: 110 + 1 = 111
  • Make sure differences stay equal: all differences = 1

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