Analyze the Number Sequence: Properties of 10, 8, 6, 4, 2

Q: Why is the common difference negative?

The common difference is negative (-2) because each term is smaller than the previous one. When numbers decrease in a sequence, the difference is always negative!

Q: What if I calculated the differences as positive?

You probably subtracted in the wrong order! Remember: later term minus earlier term. So 8-10 = -2, not 10-8 = +2.

Q: How do I know this is definitely an arithmetic sequence?

Check that all consecutive differences are the same. Since 8-10 = -2, 6-8 = -2, 4-6 = -2, and 2-4 = -2, it's definitely arithmetic!

Q: Can arithmetic sequences go backwards like this?

Absolutely! Arithmetic sequences can increase, decrease, or even stay the same. A negative common difference means the sequence decreases by the same amount each time.

Arithmetic Sequences with Negative Common Differences

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

$10,8,6,4,2$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:11 Do you see any pattern? Let's find out!

00:15 Observe how each term changes. What do you notice?

00:22 Yes, there's a pattern! Each time, we subtract 2.

00:29 And that's the solution to our 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?

$10,8,6,4,2$

Step-by-step solution

To solve this problem, we need to analyze whether the set of numbers $10, 8, 6, 4, 2$ has a pattern or property.

Step 1: Observe the difference between consecutive terms:
$8 - 10 = -2$
$6 - 8 = -2$
$4 - 6 = -2$
$2 - 4 = -2$
Step 2: Analyze the result.
We see that the difference between consecutive terms is consistently $-2$ .

This indicates that the terms form an arithmetic sequence with a common difference of $-2$ .

Hence, the property of this set of numbers is that it is an arithmetic sequence with a common difference of $-2$ .

By comparing the possible answer choices, we confirm that the correct choice is number 1: $-2$ .

Final Answer

$-2$

Key Points to Remember

Essential concepts to master this topic

Definition: Arithmetic sequence has constant difference between consecutive terms
Method: Calculate 8-10 = -2, 6-8 = -2 to find pattern
Check: Verify all consecutive differences equal -2 for confirmation ✓

Common Mistakes

Avoid these frequent errors

Calculating differences in wrong order
Don't subtract 10-8 = +2 instead of 8-10 = -2! This gives the opposite sign and makes you think the sequence is increasing when it's actually decreasing. Always subtract the previous term from the current term: second minus first.

Practice Quiz

Test your knowledge with interactive questions

Is there a term-to-term rule for the sequence below?

18 , 22 , 26 , 30

FAQ

Everything you need to know about this question

Why is the common difference negative?

The common difference is negative (-2) because each term is smaller than the previous one. When numbers decrease in a sequence, the difference is always negative!

What if I calculated the differences as positive?

You probably subtracted in the wrong order! Remember: later term minus earlier term. So 8-10 = -2, not 10-8 = +2.

How do I know this is definitely an arithmetic sequence?

Check that all consecutive differences are the same. Since 8-10 = -2, 6-8 = -2, 4-6 = -2, and 2-4 = -2, it's definitely arithmetic!

What would the next term in this sequence be?

To find the next term, add the common difference: $2 + (-2) = 0$ . The sequence continues: 10, 8, 6, 4, 2, 0, -2, -4...

Can arithmetic sequences go backwards like this?

Absolutely! Arithmetic sequences can increase, decrease, or even stay the same. A negative common difference means the sequence decreases by the same amount each time.

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