Complete the Decimal Sequence: 1, 0.9, 0.8, Missing Terms

Q: What if the differences between terms aren't the same?

Then it's not an arithmetic sequence! Arithmetic sequences have a constant difference. If differences vary, you need to look for other patterns like multiplication or more complex rules.

Q: Can I work backwards to check my answer?

Absolutely! Start with your last term and add 0.1 repeatedly: 0.5 + 0.1 = 0.6, then 0.6 + 0.1 = 0.7, then 0.7 + 0.1 = 0.8. You should get back to the given terms!

Arithmetic Sequences with Decimal Decrements

Complete the following sequence:

$\text{1,0}.9,0.8,?,?,\text{?}$

❤️ Continue Your Math Journey!

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

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 Let's verify the pattern is maintained, subtract between the following numbers

00:55 We see the difference is equal, therefore the pattern is maintained

01:06 Let's use this pattern and add the difference to find the next term

01:33 This is the next term, let's use the same method for the remaining terms

02:07 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:

$\text{1,0}.9,0.8,?,?,\text{?}$

Step-by-step solution

To solve this problem, let's determine the rule for creating the sequence:

Step 1: Identify the given numbers in the sequence: 1, 0.9, 0.8.
Step 2: Determine the difference between consecutive terms:
- From 1 to 0.9, the difference is 0.1 (i.e., 1 - 0.9 = 0.1).
- From 0.9 to 0.8, the difference is also 0.1 (i.e., 0.9 - 0.8 = 0.1).
Step 3: Notice the pattern is a decrease of 0.1 between each term.
Step 4: Apply this pattern to find the next terms:
- The next term after 0.8 is 0.8 - 0.1 = 0.7.
- Following 0.7, the next term is 0.7 - 0.1 = 0.6.
- Finally, after 0.6, the term is 0.6 - 0.1 = 0.5.

Therefore, the next three terms in the sequence are $0.7, 0.6, 0.5$ .

Final Answer

$0.7,0.6,0.5$

Key Points to Remember

Essential concepts to master this topic

Pattern Rule: Find the common difference between consecutive terms first
Technique: Subtract 0.1 from each term: 0.8 - 0.1 = 0.7
Check: Verify pattern holds: 1→0.9→0.8→0.7 all decrease by 0.1 ✓

Common Mistakes

Avoid these frequent errors

Assuming the pattern without checking differences
Don't just guess the pattern based on the first two terms = wrong sequence! You might think it's decreasing by 0.2 or increasing. Always calculate the exact difference between ALL given consecutive terms to confirm the 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 the sequence is increasing or decreasing?

Look at the direction from one term to the next! In this sequence, 1 to 0.9 goes down, and 0.9 to 0.8 also goes down, so it's decreasing by 0.1 each time.

What if the differences between terms aren't the same?

Then it's not an arithmetic sequence! Arithmetic sequences have a constant difference. If differences vary, you need to look for other patterns like multiplication or more complex rules.

Can I work backwards to check my answer?

Absolutely! Start with your last term and add 0.1 repeatedly: 0.5 + 0.1 = 0.6, then 0.6 + 0.1 = 0.7, then 0.7 + 0.1 = 0.8. You should get back to the given terms!

What if I get confused with the decimal calculations?

Try thinking of decimals as fractions: $0.1 = \frac{1}{10}$ . So subtracting 0.1 is like subtracting $\frac{1}{10}$ . You can also count down by tenths: 0.8, 0.7, 0.6, 0.5...

How many terms can this sequence have?

This sequence can continue as long as you want! It goes: 1, 0.9, 0.8, 0.7, 0.6, 0.5, 0.4, 0.3, 0.2, 0.1, 0, -0.1, -0.2... The pattern never stops!

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Decimal Fractions - Basic 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