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

Look at the following set of numbers and determine if there is any property, if so, what is it?

$$ 94,96,98,100,102,104 $$

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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