Complete the Arithmetic Sequence: From 20 to 2 in Chair Numbers

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

Look at the first few terms! In this problem, 20 becomes 18, then 16 - the numbers are getting smaller. This means we have a decreasing arithmetic sequence with a negative common difference.

Q: What if I can't see the pattern right away?

Find the difference between consecutive terms. Here: 18 - 20 = -2, and 16 - 18 = -2. When the difference is the same each time, you have an arithmetic sequence!

Q: How do I check my answer is correct?

Write out the complete sequence with your answers: 20, 18, 16, 14, 12, 10, 8, 6, 4, 2. Each number should be exactly 2 less than the previous one!

Q: Can arithmetic sequences go in both directions?

Yes! If the common difference is positive, the sequence increases. If it's negative (like $ -2 $ here), the sequence decreases. Both are perfectly valid arithmetic sequences.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:13 Let's find the missing elements.

00:16 Next, subtract each element from the next one to spot the difference.

00:21 This difference shows us the pattern in the sequence.

00:25 Now, use this pattern to calculate any missing numbers.

00:31 And that's how we solve this problem.

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

In a classroom there are 10 chairs numbered according to the constant property. Complete the series of chairs:

20 , 18

16 , 14

_ , _

8 , 6

4 , 2

2

Step-by-step solution

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

Step 1: Identify the common pattern or rule in the sequence.
Step 2: Use this pattern to determine the missing numbers.
Step 3: Verify the pattern continues correctly with the numbers found.

Now, let's work through each step:
Step 1: The sequence provided is 20, 18, 16, 14, __, __, 8, 6, 4, 2.
We notice that each number differs from the previous one by $-2$ (20 to 18, 18 to 16, etc.). This suggests an arithmetic sequence with a common difference of $-2$ .

Step 2: Let's continue this pattern to find the missing numbers. We have 16, 14, and then the blank spaces before reaching 8. So, following the pattern:
From 14, subtract 2 to get 12.
From 12, subtract 2 to get 10.
So, the missing numbers in the sequence are 12 and 10.

Step 3: Verify the sequence by checking the pattern:
Starting from 20: 20, 18, 16, 14, 12, 10, 8, 6, 4, 2.
Each step follows the pattern of subtracting 2.

Therefore, the missing numbers in the series are $12, 10$ .

3

Final Answer

12 , 10

Key Points to Remember

Essential concepts to master this topic

Pattern: Each term decreases by the same constant amount
Technique: From 14, subtract 2 to get 12, then 10
Check: Verify sequence flows: 20, 18, 16, 14, 12, 10, 8, 6, 4, 2 ✓

Common Mistakes

Avoid these frequent errors

Adding instead of subtracting the common difference
Don't add 2 to continue the pattern from 14 = 16, 18 which breaks the decreasing sequence! This happens when students focus on the number 2 but ignore the negative direction. Always identify whether the sequence increases or decreases first, then apply the common difference correctly.

Practice Quiz

Test your knowledge with interactive questions

12 ☐ 10 ☐ 8 7 6 5 4 3 2 1

Which numbers are missing from the sequence so that the sequence has a term-to-term rule?

FAQ

Everything you need to know about this question

How do I know if the sequence is increasing or decreasing?

+

Look at the first few terms! In this problem, 20 becomes 18, then 16 - the numbers are getting smaller. This means we have a decreasing arithmetic sequence with a negative common difference.

What if I can't see the pattern right away?

+

Find the difference between consecutive terms. Here: 18 - 20 = -2, and 16 - 18 = -2. When the difference is the same each time, you have an arithmetic sequence!

Why can't the missing numbers be 15, 13?

+

That would break the pattern! If we had 14, 15, 13, 8, the differences would be $+1, -2, -5$ - not constant. In arithmetic sequences, the difference must stay the same.

How do I check my answer is correct?

+

Write out the complete sequence with your answers: 20, 18, 16, 14, 12, 10, 8, 6, 4, 2. Each number should be exactly 2 less than the previous one!

Can arithmetic sequences go in both directions?

+

Yes! If the common difference is positive, the sequence increases. If it's negative (like $-2$ here), the sequence decreases. Both are perfectly valid arithmetic sequences.

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