Complete the Number Sequence: Finding Missing Terms in 20, 24, 26

Arithmetic Sequences with Even Numbers

Complete the following sequence:

20,,24,26, 20,\ldots,24,26\ldots ,\ldots

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Complete the following sequence:

20,,24,26, 20,\ldots,24,26\ldots ,\ldots

2

Step-by-step solution

To solve the problem of completing the sequence 20,,24,26,, 20, \ldots, 24, 26, \ldots, \ldots , we recognize the sequence's underlying pattern.

Step 1: Analyze known terms.
The given sequence begins with 20,,24,26,, 20, \ldots, 24, 26, \ldots, \ldots . Notice the known terms 20 20 and 24 24 , and 26 26 .

Step 2: Determine the difference between known terms.
The difference between 24 24 and 20 20 is 4 4 , suggesting an ongoing pattern.
Between 26 26 and 24 24 , the difference is 2 2 , proposing alternation in differences or a complete oversight of interspersed terms around 26 26 .

Step 3: Determine full sequence consistency.
Check if numbers align with a two-step even-number sequence, which implies adding 2 2 successively.
Extending forward and back confirms 20,22,24,26,28, 20, 22, 24, 26, 28, \ldots .

Step 4: Verification considering other instructions.
The sequence appears to be a straightforward arithmetic one comprising purely even numbers beginning from 20 20 . This step requires confirming subsequent numbers 28,30 28, 30 .

Conclusion: Sequential confirmation proves the arithmetic nature of the understanding, yielding:

20,22,24,26,28,30 20,22,24,26,28,30

3

Final Answer

20,22,24,26,28,30 20,22,24,26,28,30

Key Points to Remember

Essential concepts to master this topic
  • Pattern Recognition: Look for consistent differences between consecutive terms
  • Common Difference: Calculate 24 - 20 = 4, then 26 - 24 = 2
  • Verification: Check if pattern continues: 20, 22, 24, 26, 28, 30 ✓

Common Mistakes

Avoid these frequent errors
  • Assuming the pattern continues with the same difference as the first gap
    Don't assume the difference stays 4 throughout = wrong sequence 20, 24, 28, 32! This misses that 26 follows 24, not 28. Always check all given terms to find the true pattern.

Practice Quiz

Test your knowledge with interactive questions

Complete the following sequence:

\( 20,\ldots,24,26\ldots ,\ldots \)

FAQ

Everything you need to know about this question

Why isn't the difference always 4 like between 20 and 24?

+

The key is recognizing this is a sequence of consecutive even numbers! The gap between 20 and 24 skips 22, but the actual pattern is add 2 each time: 20, 22, 24, 26, 28, 30.

How do I know which numbers are missing?

+

Look at the complete pattern first. Since we have even numbers with differences of 2, work backwards and forwards: 20 + 2 = 22, then 22 + 2 = 24, and so on.

What if I see different patterns in the same sequence?

+

Always use all given information! Here, 20, 24, 26 tells us it's consecutive evens, not jumps of 4. The missing 22 between 20 and 24 is the clue.

How can I check my answer is correct?

+

Verify that your sequence has a consistent pattern. For 20,22,24,26,28,30 20, 22, 24, 26, 28, 30 , each difference is 2, and all given terms (20, 24, 26) appear in the right positions.

Are there other ways to complete this sequence?

+

While other mathematical patterns are possible, the most logical and simple completion is consecutive even numbers. This matches all given terms with the smallest, most consistent rule.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Magnitude up to 100 questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

More Questions

Click on any question to see the complete solution with step-by-step explanations