Analyze the Number Sequence: Finding Properties in 94, 96, 98, 100, 102, 104

Q: How do I know if there's really a pattern in the numbers?

Calculate the difference between each consecutive pair. If all differences are the same, you have an arithmetic sequence! If they vary, look for other patterns like multiplication or squares.

Q: What if I get different differences between some pairs?

Then it's not an arithmetic sequence! Check your subtraction carefully first. If the differences are truly different, the sequence might have a different type of pattern or no pattern at all.

Q: Why do we subtract the first number from the second?

We always subtract in order: next term minus previous term. This shows how much the sequence increases (positive difference) or decreases (negative difference) at each step.

Q: Can arithmetic sequences have negative differences?

Absolutely! If each term is smaller than the previous one, you'll get negative differences. For example: 10, 7, 4, 1 has a common difference of -3.

Q: What makes this sequence special compared to other number lists?

This sequence has a constant difference of +2, making it an arithmetic sequence. Plus, all terms are even numbers, which makes the pattern even more regular and predictable.

Arithmetic Sequences with Even Numbers

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

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

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:12 Do you notice any pattern here? What might it be?

00:15 Let's take a closer look at how the terms change.

00:26 Can you see it now? The pattern stays the same. We keep adding 2 each time.

00:32 And there you have it. That's how we solve the question!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

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

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

Step-by-step solution

One can observe that the difference between each number is 2.

That is, with each leap the next number increases by 2:

$94+2=96$

$96+2=98$

$98+2=100$

and so forth......

Final Answer

$+2$

Key Points to Remember

Essential concepts to master this topic

Pattern Recognition: Look for constant differences between consecutive terms
Technique: Calculate differences: 96-94=2, 98-96=2, 100-98=2
Check: Verify every consecutive pair has same difference: all equal 2 ✓

Common Mistakes

Avoid these frequent errors

Assuming the pattern is addition without checking differences
Don't just guess +2 without calculating each difference = wrong pattern identification! You might miss that some sequences change their pattern. Always subtract each consecutive pair to verify the constant difference.

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 there's really a pattern in the numbers?

Calculate the difference between each consecutive pair. If all differences are the same, you have an arithmetic sequence! If they vary, look for other patterns like multiplication or squares.

What if I get different differences between some pairs?

Then it's not an arithmetic sequence! Check your subtraction carefully first. If the differences are truly different, the sequence might have a different type of pattern or no pattern at all.

Why do we subtract the first number from the second?

We always subtract in order: next term minus previous term. This shows how much the sequence increases (positive difference) or decreases (negative difference) at each step.

Can arithmetic sequences have negative differences?

Absolutely! If each term is smaller than the previous one, you'll get negative differences. For example: 10, 7, 4, 1 has a common difference of -3.

What makes this sequence special compared to other number lists?

This sequence has a constant difference of +2, making it an arithmetic sequence. Plus, all terms are even numbers, which makes the pattern even more regular and predictable.

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