Complete the Decimal Sequence: Finding Missing Terms in 1, 0.8, 0.6, ?, ?

Q: How do I know if it's an arithmetic sequence?

Check if the difference between consecutive terms stays the same. In this problem: $ 1 - 0.8 = 0.2 $ and $ 0.8 - 0.6 = 0.2 $, so it's arithmetic!

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

Then it might be a geometric sequence (multiply/divide) or another pattern. Try finding what you multiply each term by, or look for other relationships like squares or cubes.

Q: Can arithmetic sequences go negative?

Yes! If you keep subtracting $ 0.2 $ from this sequence, you'll get: 0.4, 0.2, 0, -0.2, -0.4 and so on. The pattern continues!

Q: Why do we subtract instead of add in this problem?

Look at the numbers: $ 1, 0.8, 0.6 $ are decreasing. This means we subtract the same amount each time. If they were increasing, we'd add the same amount.

Q: How can I double-check my answer?

Use the pattern to find one more term! If $ 0.4, 0.2 $ is correct, then $ 0.2 - 0.2 = 0 $ should be the next term. Does this make sense? Yes!

Arithmetic Sequences with Decimal Patterns

Complete the following sequence:

$1,0.8,0.6,?,\text{?}$

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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.

00:14 First, subtract between the numbers. This will help us find the difference.

00:46 Great job! This is the difference between the terms.

00:59 Now, let’s check if this pattern continues. Subtract between the next numbers.

01:20 We see that the difference remains the same. So, the pattern holds.

01:33 Let's use this pattern now. Add the difference to find the next term.

01:58 This is the next term. Let's use the same method for the rest of the terms.

02:34 And there you have it! That's the solution to our question.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Complete the following sequence:

$1,0.8,0.6,?,\text{?}$

Step-by-step solution

To solve this problem, we'll look for a consistent pattern in the given sequence:

Step 1: Identify the difference between consecutive terms.
- From $1$ to $0.8$ , the difference is $0.2$ (i.e., $1 - 0.8 = 0.2$ ).
- From $0.8$ to $0.6$ , the difference is $0.2$ (i.e., $0.8 - 0.6 = 0.2$ ).
Step 2: Determine the next terms using this difference.
- The next term after $0.6$ will be $0.6 - 0.2 = 0.4$ .
- The term after that will be $0.4 - 0.2 = 0.2$ .

Therefore, the sequence $1, 0.8, 0.6, ?, ?$ continues as $0.4, 0.2$ .

The correct answer is $0.4, 0.2$ , which corresponds to choice 4.

Final Answer

$0.4,0.2$

Key Points to Remember

Essential concepts to master this topic

Pattern Recognition: Find consistent difference between consecutive terms
Technique: Subtract each term: $1 - 0.8 = 0.2$
Check: Verify pattern continues: $0.6 - 0.2 = 0.4$ ✓

Common Mistakes

Avoid these frequent errors

Looking for multiplication patterns instead of subtraction
Don't try to find what each term multiplies by = confusing patterns! This leads to wrong answers because decimal sequences often use addition/subtraction. Always check differences between consecutive terms first.

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 an arithmetic sequence?

Check if the difference between consecutive terms stays the same. In this problem: $1 - 0.8 = 0.2$ and $0.8 - 0.6 = 0.2$ , so it's arithmetic!

What if the differences aren't the same?

Then it might be a geometric sequence (multiply/divide) or another pattern. Try finding what you multiply each term by, or look for other relationships like squares or cubes.

Can arithmetic sequences go negative?

Yes! If you keep subtracting $0.2$ from this sequence, you'll get: 0.4, 0.2, 0, -0.2, -0.4 and so on. The pattern continues!

Why do we subtract instead of add in this problem?

Look at the numbers: $1, 0.8, 0.6$ are decreasing. This means we subtract the same amount each time. If they were increasing, we'd add the same amount.

How can I double-check my answer?

Use the pattern to find one more term! If $0.4, 0.2$ is correct, then $0.2 - 0.2 = 0$ should be the next term. Does this make sense? Yes!

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