Complete the Arithmetic Sequence: Finding Missing Numbers in 0, 2, 4, 6, 8, 10 Pattern

Arithmetic Sequences with Even Number Patterns

Fill in the missing number

000222444666888101010

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1

Understand the problem

Fill in the missing number

000222444666888101010

2

Step-by-step solution

Let's look at the numbers from left to right:

0,2,4,6,8 0,2,4,6,8

We notice that the common operation is +2:

0+2=2 0+2=2

2+2=4 2+2=4

4+2=6 4+2=6

6+2=8 6+2=8

8+2=10 8+2=10

Therefore, the next sequence will be:

10+2=12 10+2=12

12+2=14 12+2=14

14+2=16 14+2=16

16+2=18 16+2=18

3

Final Answer

18, 16, 14, 12

Key Points to Remember

Essential concepts to master this topic
  • Pattern Recognition: Each term increases by the same constant difference
  • Technique: Add common difference 2: 10+2=12, 12+2=14, 14+2=16, 16+2=18
  • Check: Verify pattern holds: 0,2,4,6,8,10,12,14,16,18 increases by 2 each time ✓

Common Mistakes

Avoid these frequent errors
  • Adding wrong amounts or random numbers
    Don't add different amounts like +2, then +3, then +1 = broken pattern! This creates inconsistent sequences that don't follow the arithmetic rule. Always identify the common difference first and add the same amount every time.

Practice Quiz

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All negative numbers appear on the number line to the left of the number 0.

FAQ

Everything you need to know about this question

How do I find the pattern in a sequence?

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Look at the difference between consecutive terms. In this sequence: 2-0=2, 4-2=2, 6-4=2. Since the difference is always 2, that's your pattern!

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

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Try calculating the differences between each pair of numbers. Write them down: 0 to 2 (+2), 2 to 4 (+2), 4 to 6 (+2). When you see the same difference repeating, you've found your pattern!

Are there other types of number patterns?

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Yes! Some patterns multiply by the same number each time, or add increasing amounts. But arithmetic sequences like this one always add (or subtract) the same amount.

How many numbers should I continue the pattern?

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Count the empty spaces in the diagram or follow the question instructions. Here we have 4 empty positions, so we need the next 4 numbers: 12, 14, 16, 18.

What if the pattern goes backwards?

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Some arithmetic sequences decrease by the same amount each time. For example: 20, 18, 16, 14... The common difference would be -2 instead of +2.

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