Find the Term-to-Term Rule: Analyzing Sequence 18, 22, 26, 30

Arithmetic Sequences with Constant Differences

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

18 , 22 , 26 , 30

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:07 Do you see a pattern here? Let's find out!
00:11 Notice how each term is 4 less than the one before it.
00:18 So, the pattern is to subtract 4 each time.
00:22 And that's how we solve this question!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

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

18 , 22 , 26 , 30

2

Step-by-step solution

To solve this problem, we'll check the differences between consecutive terms:

  • The difference between 2222 and 1818 is 2218=422 - 18 = 4.
  • The difference between 2626 and 2222 is 2622=426 - 22 = 4.
  • The difference between 3030 and 2626 is 3026=430 - 26 = 4.

All differences between consecutive terms are 44, indicating a constant increment. Thus, the sequence is arithmetic with a common difference of 44.

The term-to-term rule is: to get the next term, add 44 to the current term.

Therefore, yes, there is a term-to-term rule for this sequence, given by adding 44 to the previous term.

3

Final Answer

Yes

Key Points to Remember

Essential concepts to master this topic
  • Rule: Term-to-term rule exists when consecutive differences are constant
  • Technique: Calculate differences: 22-18=4, 26-22=4, 30-26=4
  • Check: All differences equal 4, so add 4 to get next term ✓

Common Mistakes

Avoid these frequent errors
  • Assuming no pattern exists without checking differences
    Don't just look at the numbers without calculating differences = missing obvious patterns! Numbers like 18, 22, 26, 30 might seem random at first glance. Always subtract consecutive terms to find the common difference and identify arithmetic sequences.

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

What exactly is a term-to-term rule?

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A term-to-term rule tells you how to get from one term to the next in a sequence. For this sequence, the rule is add 4 to the previous term to get the next one.

How do I know if differences are constant?

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Calculate the difference between each pair of consecutive terms. If all differences are the same number, then you have a constant difference and an arithmetic sequence!

What if the differences aren't all the same?

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Then there's no simple term-to-term rule for that sequence. You might need to look for other patterns, like second differences or geometric relationships.

Can I use this rule to find more terms?

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Absolutely! Once you know the rule is add 4, you can find any term: the 5th term would be 30 + 4 = 34, the 6th term would be 34 + 4 = 38, and so on.

What if I get negative differences?

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That's perfectly fine! A negative common difference means the sequence is decreasing. For example, if differences are all -3, your rule would be subtract 3 from the previous term.

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