Complete the Decimal Sequence: Finding Next Terms After 0, 0.2, 0.4, 0.6

Q: How do I know if a sequence is arithmetic?

Check if the difference between consecutive terms is always the same. In this sequence: $ 0.2-0 = 0.2 $, $ 0.4-0.2 = 0.2 $, $ 0.6-0.4 = 0.2 $. Same difference = arithmetic sequence!

Q: What if I get confused by the decimals?

Think of decimals as fractions! $ 0.2 = \frac{2}{10} $, so you're adding $ \frac{2}{10} $ each time. Or convert to whole numbers: 0, 2, 4, 6, ?, ? becomes much easier!

Q: Can the common difference be negative?

Yes! If each term gets smaller by the same amount, that's still an arithmetic sequence. For example: $ 1, 0.8, 0.6, 0.4 $ has a common difference of $ -0.2 $.

Q: What if the differences aren't exactly the same?

Then it's not an arithmetic sequence! Double-check your calculations. Small rounding errors can happen, but the pattern should be clearly consistent in these problems.

Arithmetic Sequences with Decimal Increments

Complete the following sequence:

$0,0.2,0.4,0.6,?,\text{?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Complete the sequence

00:07 Subtract between the numbers to find the difference

00:27 This is the difference between terms

00:34 Let's verify the pattern holds, subtract between the following numbers

01:01 We see the difference is equal, so the pattern holds

01:18 Let's use this pattern and add the difference to find the next term

01:46 This is the next term, let's use the same method for the remaining terms

02:25 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Complete the following sequence:

$0,0.2,0.4,0.6,?,\text{?}$

Step-by-step solution

To determine the next numbers in the sequence $0, 0.2, 0.4, 0.6$ , we proceed by identifying the pattern:

Evaluate the difference between the first two terms: $0.2 - 0 = 0.2$ .
Verify this difference remains the same between the subsequent terms: $0.4 - 0.2 = 0.2$ and $0.6 - 0.4 = 0.2$ .

Each term increases by $0.2$ . Therefore, this sequence follows an arithmetic progression with a common difference of $0.2$ .

To find the next term in the sequence: add $0.2$ to the last known term.

Next term after $0.6$ is $0.6 + 0.2 = 0.8$ .
To find the term following $0.8$ , add $0.2$ again: $0.8 + 0.2 = 1$ .

Thus, the next two numbers in the sequence are $0.8$ and $1$ .

The correct answer, therefore, is $0.8, 1$ .

Final Answer

$0.8,1$

Key Points to Remember

Essential concepts to master this topic

Pattern Recognition: Find the common difference between consecutive terms
Technique: Calculate $0.6 + 0.2 = 0.8$ , then $0.8 + 0.2 = 1$
Check: Verify each term increases by exactly $0.2$ throughout the sequence ✓

Common Mistakes

Avoid these frequent errors

Assuming the pattern changes or gets more complex
Don't overthink simple patterns like adding 0.1 or 0.3 instead of 0.2 = wrong sequence! Students often assume sequences must get harder or follow complex rules. Always stick to the consistent difference you identify first.

Practice Quiz

Test your knowledge with interactive questions

Determine the numerical value of the shaded area:

FAQ

Everything you need to know about this question

How do I know if a sequence is arithmetic?

Check if the difference between consecutive terms is always the same. In this sequence: $0.2-0 = 0.2$ , $0.4-0.2 = 0.2$ , $0.6-0.4 = 0.2$ . Same difference = arithmetic sequence!

What if I get confused by the decimals?

Think of decimals as fractions! $0.2 = \frac{2}{10}$ , so you're adding $\frac{2}{10}$ each time. Or convert to whole numbers: 0, 2, 4, 6, ?, ? becomes much easier!

Can the common difference be negative?

Yes! If each term gets smaller by the same amount, that's still an arithmetic sequence. For example: $1, 0.8, 0.6, 0.4$ has a common difference of $-0.2$ .

How many terms ahead can I predict?

As many as you want! Once you know the common difference, you can find any term. The formula is: next term = current term + common difference.

What if the differences aren't exactly the same?

Then it's not an arithmetic sequence! Double-check your calculations. Small rounding errors can happen, but the pattern should be clearly consistent in these problems.

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