Complete the Decimal Sequence: Finding Missing Terms in 0.9, 0.6, ?, ?

Q: How do I know if it's adding or subtracting?

Look at whether the numbers are getting bigger or smaller. Since 0.9 becomes 0.6, the sequence is decreasing, so we're subtracting the same amount each time.

Q: Could this be a different type of pattern, like multiplication?

Always check the simplest pattern first! Since $ 0.9 - 0.6 = 0.3 $ gives us a clear constant difference, this is an arithmetic sequence (adding/subtracting the same amount).

Q: How do I check my answer is right?

Make sure your sequence has the same difference between every pair of consecutive terms. Here: 0.9→0.6 (-0.3), 0.6→0.3 (-0.3), 0.3→0 (-0.3) ✓

Arithmetic Sequences with Decimal Differences

Complete the following sequence:

$0.9,0.6,?,\text{?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Complete the sequence

00:04 Subtract between the numbers to find the difference

00:27 This is the difference between terms

00:39 We'll use this pattern and add the difference to find the next term

01:16 This is the next term, we'll use the same method for the remaining terms

01:50 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:

$0.9,0.6,?,\text{?}$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Identify the sequence pattern.
Step 2: Calculate the differences between known terms.
Step 3: Use the difference to find missing terms.
Step 4: Validate against the given choices.

Now, let's work through each step:
Step 1: Identify the sequence pattern from the given terms $0.9$ and $0.6$ .
Step 2: Calculate the difference between $0.9$ and $0.6$ , which is $0.9 - 0.6 = 0.3$ . This indicates the sequence decreases by $0.3$ with each term.
Step 3: Apply this difference to find the next terms:
- Subtract $0.3$ from $0.6$ : $0.6 - 0.3 = 0.3$
- Subtract $0.3$ from $0.3$ : $0.3 - 0.3 = 0$
Step 4: Validate against the given choices; the only choice that matches this sequence is $0.3, 0$ .

Therefore, the solution to the problem is $0.3, 0$ .

Final Answer

$0.3,0$

Key Points to Remember

Essential concepts to master this topic

Pattern Recognition: Find the common difference by subtracting consecutive terms
Technique: Calculate $0.9 - 0.6 = 0.3$ to identify the pattern
Verification: Check that each term decreases by exactly 0.3: 0.9, 0.6, 0.3, 0 ✓

Common Mistakes

Avoid these frequent errors

Assuming the pattern without calculating
Don't guess the pattern by looking at just two numbers = wrong sequence! Students often assume it's dividing or using complex rules. Always calculate the actual difference between consecutive terms to find the true pattern.

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 it's adding or subtracting?

Look at whether the numbers are getting bigger or smaller. Since 0.9 becomes 0.6, the sequence is decreasing, so we're subtracting the same amount each time.

What if the difference isn't a nice round number?

That's okay! Just calculate carefully. For example, if you had 1.7, 1.3, the difference would be $1.7 - 1.3 = 0.4$ . Use whatever difference you get from the calculation.

Could this be a different type of pattern, like multiplication?

Always check the simplest pattern first! Since $0.9 - 0.6 = 0.3$ gives us a clear constant difference, this is an arithmetic sequence (adding/subtracting the same amount).

How do I check my answer is right?

Make sure your sequence has the same difference between every pair of consecutive terms. Here: 0.9→0.6 (-0.3), 0.6→0.3 (-0.3), 0.3→0 (-0.3) ✓

What if I get a negative number in my sequence?

That's perfectly normal! If the pattern continues decreasing, you might get negative numbers. Just keep subtracting the same amount: 0, -0.3, -0.6, and so on.

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