Complete the Sequence: Finding the Pattern in 36, 34, ...

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

Check if the difference between consecutive terms is constant. In this case, $ 36 - 34 = 2 $, so if it continues decreasing by 2, it's arithmetic!

Q: What if I can't see the pattern with just two terms?

With only two terms, assume the simplest pattern first - a constant difference. Look at $ 36 - 34 = 2 $ and continue subtracting 2 from each term.

Q: Could this sequence have a different pattern?

While other patterns are possible, arithmetic sequences with constant differences are the most common in basic math. Always try the simplest explanation first!

Arithmetic Sequences with Constant Differences

Complete the sequence:

$36,34\ldots$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Complete the sequence:

$36,34\ldots$

Step-by-step solution

To complete the given sequence $36, 34, \ldots$ , we need to identify the pattern in the sequence. From the given terms, it appears that the sequence is decreasing.

Let's check if this is an arithmetic sequence, where each term decreases by a constant amount:

Subtract the second term from the first term: $36 - 34 = 2$ .
This indicates that each term is decreasing by 2.

Recognizing this pattern, the sequence can be continued by subtracting 2 from each subsequent term:

The next term after 34 is calculated as follows: $34 - 2 = 32$ .
Continuing, the term after 32 is: $32 - 2 = 30$ .
Finally, the term following 30 is: $30 - 2 = 28$ .

Therefore, the complete sequence is $36, 34, 32, 30, 28$ .

The correct answer choice, which matches this sequence, is:

$36,34,32,30,28$

Final Answer

$36,34,32,30,28$

Key Points to Remember

Essential concepts to master this topic

Pattern Rule: Find the common difference between consecutive terms
Technique: Calculate $36 - 34 = 2$ to find constant difference
Check: Verify each term decreases by 2: 34-2=32, 32-2=30, 30-2=28 ✓

Common Mistakes

Avoid these frequent errors

Assuming different patterns without checking consistency
Don't guess random patterns like alternating increases and decreases = inconsistent sequence! This ignores the mathematical relationship between terms. Always calculate the difference between consecutive terms first to identify the constant pattern.

Practice Quiz

Test your knowledge with interactive questions

Complete the following sequence:

$20,\ldots,24,26\ldots ,\ldots$

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 is constant. In this case, $36 - 34 = 2$ , so if it continues decreasing by 2, it's arithmetic!

What if I can't see the pattern with just two terms?

With only two terms, assume the simplest pattern first - a constant difference. Look at $36 - 34 = 2$ and continue subtracting 2 from each term.

Could this sequence have a different pattern?

While other patterns are possible, arithmetic sequences with constant differences are the most common in basic math. Always try the simplest explanation first!

How do I continue the sequence beyond 5 terms?

Keep applying the same rule! After 28, the next term would be $28 - 2 = 26$ , then $26 - 2 = 24$ , and so on.

What if the difference was positive instead?

If the first term was smaller than the second (like 34, 36), you'd add the common difference instead of subtract. Same process, different direction!

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