Complete the Decimal Sequence: 0.2, 0.3, 0.4, and Three Missing Terms

Q: How do I know if a sequence has a pattern?

Look for a consistent difference between consecutive terms. In this sequence, $ 0.3 - 0.2 = 0.1 $ and $ 0.4 - 0.3 = 0.1 $, so the pattern is adding $ 0.1 $ each time!

Q: What if I get confused with decimal addition?

Line up the decimal points when adding! For example: $ 0.4 + 0.1 $ becomes 0.4 + 0.1 = 0.5. The decimal stays in the same position.

Q: Can sequences have negative differences?

Absolutely! If each term gets smaller, you subtract instead of add. For example: 0.7, 0.6, 0.5 has a difference of $ -0.1 $.

Q: How do I check if my sequence is correct?

Verify that every consecutive pair has the same difference. Check: $ 0.6 - 0.5 = 0.1 $ and $ 0.7 - 0.6 = 0.1 $. All differences should match!

Decimal Sequences with Constant Differences

Complete the following sequence:

$0.2,0.3,0.4,?,?,?$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:07 Let's complete the sequence together.

00:14 First, subtract the numbers to find the difference.

00:28 This is how we find the difference between terms.

00:33 Now, let's check if the pattern continues by subtracting the next n umbers.

00:55 The differences are equal, so the pattern does continue.

01:06 Great! Add the difference to find the next term.

01:31 This gives us the next term. Use this method for the other terms.

02:42 And that's how we solve the sequence! Well done!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Complete the following sequence:

$0.2,0.3,0.4,?,?,?$

Step-by-step solution

To solve this problem, let's identify the pattern in the sequence:

Given sequence: $0.2, 0.3, 0.4$ .

Step 1: Determine the pattern:

The first number is $0.2$ , the second number is $0.3$ , and the third number is $0.4$ .
Calculate the difference between consecutive terms: $0.3 - 0.2 = 0.1$ and $0.4 - 0.3 = 0.1$ .
Therefore, the sequence increases by $0.1$ each time.

Step 2: Use this difference to find the missing terms:

The next term after $0.4$ will be $0.4 + 0.1 = 0.5$ .
The next term after $0.5$ will be $0.5 + 0.1 = 0.6$ .
The next term after $0.6$ will be $0.6 + 0.1 = 0.7$ .

Thus, the completed sequence is $0.2, 0.3, 0.4, 0.5, 0.6, 0.7$ .

Comparing the given choices, the correct sequence is choice 3: $0.5, 0.6, 0.7$ .

Therefore, the missing terms are $0.5, 0.6, 0.7$ .

Final Answer

$0.5,0.6,0.7$

Key Points to Remember

Essential concepts to master this topic

Pattern Rule: Find the common difference between consecutive terms
Technique: Add $0.1$ repeatedly: $0.4 + 0.1 = 0.5$
Check: Verify each difference equals $0.1$ : $0.5 - 0.4 = 0.1$ ✓

Common Mistakes

Avoid these frequent errors

Looking at random differences instead of consecutive terms
Don't compare non-consecutive terms like $0.4 - 0.2 = 0.2$ and assume the pattern is +0.2! This skips terms and gives wrong answers. Always find the difference between terms that are right next to each other.

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 has a pattern?

Look for a consistent difference between consecutive terms. In this sequence, $0.3 - 0.2 = 0.1$ and $0.4 - 0.3 = 0.1$ , so the pattern is adding $0.1$ each time!

What if I get confused with decimal addition?

Line up the decimal points when adding! For example: $0.4 + 0.1$ becomes 0.4 + 0.1 = 0.5. The decimal stays in the same position.

Can sequences have negative differences?

Absolutely! If each term gets smaller, you subtract instead of add. For example: 0.7, 0.6, 0.5 has a difference of $-0.1$ .

How do I check if my sequence is correct?

Verify that every consecutive pair has the same difference. Check: $0.6 - 0.5 = 0.1$ and $0.7 - 0.6 = 0.1$ . All differences should match!

What if the pattern isn't adding the same number?

Some sequences multiply, square, or follow other rules. But for this type, always check addition/subtraction patterns first since they're most common in basic sequences.

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