Complete the Decimal Sequence: 0.9, 0.8, 0.7, Find the Next Three Terms

Q: How do I know if a sequence is increasing or decreasing?

Look at the first few terms! If each number gets smaller (like 0.9→0.8→0.7), the sequence is decreasing. If each gets larger, it's increasing.

Q: What if the common difference isn't obvious?

Always calculate it step by step! Subtract the first term from the second, then the second from the third. If you get the same answer both times, that's your common difference.

Q: What if I accidentally use the wrong common difference?

Your sequence won't match the given terms! Always double-check by verifying that your common difference works for all the given terms before continuing.

Q: How many decimal places should I use?

Use the same number of decimal places as the given terms. Since 0.9, 0.8, 0.7 have one decimal place, your answers should too: 0.6, 0.5, 0.4.

Arithmetic Sequences with Decimal Terms

Complete the following sequence:

$0.9,0.8,0.7,?,?,\text{?}$

❤️ 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

00:22 This is the difference between terms

00:31 Let's verify the pattern is maintained, subtract between the following numbers

00:52 We see the difference is equal, therefore the pattern is maintained

01:03 Let's use this pattern and add the difference to find the next term

01:27 This is the next term, let's use the same method for the remaining terms

02:26 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:

$0.9,0.8,0.7,?,?,\text{?}$

Step-by-step solution

To determine the sequence's missing numbers, follow these steps:

Step 1: Analyze the given sequence: $0.9, 0.8, 0.7$ .
Step 2: Calculate the common difference by subtracting consecutive terms. For instance, $0.8 - 0.9 = -0.1$ and $0.7 - 0.8 = -0.1$ , confirming a common difference of $-0.1$ .
Step 3: Continue the pattern using this common difference: - Starting from $0.7$ , subtract $0.1$ , giving $0.6$ as the next number. - From $0.6$ , subtract $0.1$ again, resulting in $0.5$ . - Finally, subtract $0.1$ from $0.5$ , yielding $0.4$ .

Thus, the completed sequence is $0.9, 0.8, 0.7, 0.6, 0.5, 0.4$ .

The correct answer to complete the sequence is $0.6, 0.5, 0.4$ .

Final Answer

$0.6,0.5,0.4$

Key Points to Remember

Essential concepts to master this topic

Pattern Recognition: Find the common difference between consecutive terms
Technique: Calculate $0.8 - 0.9 = -0.1$ to identify pattern
Check: Verify each term decreases by exactly 0.1: 0.7→0.6→0.5→0.4 ✓

Common Mistakes

Avoid these frequent errors

Adding instead of subtracting the common difference
Don't add 0.1 to continue the pattern = 0.8, 0.9, 1.0! This reverses the sequence direction completely. Always subtract the common difference when the sequence is decreasing.

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 increasing or decreasing?

Look at the first few terms! If each number gets smaller (like 0.9→0.8→0.7), the sequence is decreasing. If each gets larger, it's increasing.

What if the common difference isn't obvious?

Always calculate it step by step! Subtract the first term from the second, then the second from the third. If you get the same answer both times, that's your common difference.

Can decimal sequences have different patterns?

Yes! Some sequences multiply by a factor, others follow more complex rules. But arithmetic sequences like this one always add or subtract the same amount each time.

What if I accidentally use the wrong common difference?

Your sequence won't match the given terms! Always double-check by verifying that your common difference works for all the given terms before continuing.

How many decimal places should I use?

Use the same number of decimal places as the given terms. Since 0.9, 0.8, 0.7 have one decimal place, your answers should too: 0.6, 0.5, 0.4.

🌟 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