Complete the Decimal Sequence: 0.5, 0.6, 0.7, Finding the Next Three Terms

Q: How do I know what the pattern is in a decimal sequence?

Look at the difference between consecutive terms. In this sequence: 0.6 - 0.5 = 0.1 and 0.7 - 0.6 = 0.1. Since the difference is always $ 0.1 $, add 0.1 to continue the pattern.

Q: Why is the last term 1 instead of 1.0?

Both 1 and 1.0 represent the same value! In mathematics, we often write whole numbers without the decimal point for simplicity. So $ 1 = 1.0 = 1.00 $.

Q: What if I accidentally wrote 0.10 instead of 1.0?

Be careful! $ 0.10 = 0.1 $, which is much smaller than 1.0. Remember that $ 0.9 + 0.1 = 1.0 $, not 0.10. The zero after the decimal point matters!

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

Verify that each step increases by the same amount. Calculate: 0.8 - 0.7 = 0.1, then 0.9 - 0.8 = 0.1, and finally 1.0 - 0.9 = 0.1. All differences should be equal!

Q: Are there other types of decimal sequences?

Yes! Some sequences might increase by $ 0.2 $, $ 0.5 $, or even decrease. The key is to identify the pattern by finding what's being added or subtracted each time.

Arithmetic Sequences with Decimal Increments

Complete the following sequence:

$0.5,0.6,0.7,?,?,\text{?}$

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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

00:36 Let's verify the pattern holds, subtract between the following numbers

00:58 We see the difference is equal, therefore the pattern holds

01:14 Let's use this pattern and add the difference to find the next term

01:49 This is the next term, let's use the same method for the remaining terms

03:11 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:

$0.5,0.6,0.7,?,?,\text{?}$

Step-by-step solution

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

Step 1: Identify the pattern in the given sequence.
Step 2: Continue the pattern to find the missing terms.

Now, let's work through each step:

Step 1: Look at the given sequence: $0.5, 0.6, 0.7$ . We notice that each term increases by $0.1$ .

Step 2: To continue the pattern, add $0.1$ to the last given term, $0.7$ :

Next term: $0.7 + 0.1 = 0.8$
Next term after $0.8$ : $0.8 + 0.1 = 0.9$
Final term to find: $0.9 + 0.1 = 1.0$

Therefore, the complete sequence is: $0.5, 0.6, 0.7, 0.8, 0.9, 1$ .

We can verify this matches choice number 1 in the provided answers:

$0.8, 0.9, 1$ .

Final Answer

$0.8,0.9,1$

Key Points to Remember

Essential concepts to master this topic

Pattern Recognition: Find the common difference between consecutive terms
Technique: Add 0.1 to each term: 0.7 + 0.1 = 0.8
Check: Verify each term increases by same amount: 0.5→0.6→0.7→0.8→0.9→1.0 ✓

Common Mistakes

Avoid these frequent errors

Writing 1.0 as 0.10 in the final position
Don't write 1.0 as 0.10 = completely different values! 0.10 equals 0.1, not 1. Always remember that 0.9 + 0.1 = 1.0, and 1.0 is the standard way to write the whole number one as a decimal.

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 what the pattern is in a decimal sequence?

Look at the difference between consecutive terms. In this sequence: 0.6 - 0.5 = 0.1 and 0.7 - 0.6 = 0.1. Since the difference is always $0.1$ , add 0.1 to continue the pattern.

Why is the last term 1 instead of 1.0?

Both 1 and 1.0 represent the same value! In mathematics, we often write whole numbers without the decimal point for simplicity. So $1 = 1.0 = 1.00$ .

What if I accidentally wrote 0.10 instead of 1.0?

Be careful! $0.10 = 0.1$ , which is much smaller than 1.0. Remember that $0.9 + 0.1 = 1.0$ , not 0.10. The zero after the decimal point matters!

How can I check if my sequence is correct?

Verify that each step increases by the same amount. Calculate: 0.8 - 0.7 = 0.1, then 0.9 - 0.8 = 0.1, and finally 1.0 - 0.9 = 0.1. All differences should be equal!

Are there other types of decimal sequences?

Yes! Some sequences might increase by $0.2$ , $0.5$ , or even decrease. The key is to identify the pattern by finding what's being added or subtracted each time.

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