Analyze the Sequence: Finding the Term-to-Term Rule for 64, 85, 98, 100, 1

Q: Why can't I just use the most common difference?

Because a term-to-term rule must work for every single step in the sequence! If even one step is different, there's no consistent rule. In this sequence, we have differences of 21, 13, 2, and -99 - clearly no pattern.

Q: How do I avoid getting tricked by sequences like this?

Always calculate ALL the differences first! Don't assume there's a pattern. Look at: $85-64=21$, $98-85=13$, $100-98=2$, $1-100=-99$. These are completely different!

Q: What if the differences were closer together?

Even if differences were similar but not identical (like 5, 6, 5, 7), there would still be no consistent term-to-term rule. The operation must be exactly the same each time.

Sequence Analysis with Irregular Patterns

Look at the following sequence:

64 , 85 , 98 , 100 , 1

Is there a term-to-term rule?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Is there any pattern in the sequence?

00:04 Let's examine the change between terms

00:11 We can see that the change is not constant, therefore there is no pattern

00:19 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Look at the following sequence:

64 , 85 , 98 , 100 , 1

Is there a term-to-term rule?

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Examine differences between consecutive terms
Step 2: Check for consistency in differences

Let's calculate the differences:

$85 - 64 = 21$

$98 - 85 = 13$

$100 - 98 = 2$

$1 - 100 = -99$

Observing these differences, it is evident that they are not consistent. Therefore, there is no consistent arithmetic or geometric pattern that applies to the entire sequence. Given the choices, the conclusion is clear: There is no term-to-term rule.

Therefore, the correct answer choice is 4: No.

Final Answer

No.

Key Points to Remember

Essential concepts to master this topic

Term-to-term rule: Same operation applied between all consecutive terms consistently
Technique: Calculate differences: 85-64=21, 98-85=13, 100-98=2, 1-100=-99
Check: If differences vary (21, 13, 2, -99), no consistent rule exists ✓

Common Mistakes

Avoid these frequent errors

Assuming every sequence must have a pattern
Don't try to force a rule when differences are completely inconsistent = wrong conclusions! Students often pick the most common difference or ignore obvious outliers. Always calculate ALL consecutive differences and verify they follow the same pattern throughout.

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?

A term-to-term rule is when you can get from one term to the next using the same operation every time. For example, +3, +3, +3... or ×2, ×2, ×2...

Why can't I just use the most common difference?

Because a term-to-term rule must work for every single step in the sequence! If even one step is different, there's no consistent rule. In this sequence, we have differences of 21, 13, 2, and -99 - clearly no pattern.

Could there be a different type of pattern I'm missing?

While sequences can have complex patterns, the question asks specifically for a term-to-term rule. This means a simple, consistent operation between consecutive terms. More complex patterns exist, but that's not what we're looking for here.

How do I avoid getting tricked by sequences like this?

Always calculate ALL the differences first! Don't assume there's a pattern. Look at: $85-64=21$ , $98-85=13$ , $100-98=2$ , $1-100=-99$ . These are completely different!

What if the differences were closer together?

Even if differences were similar but not identical (like 5, 6, 5, 7), there would still be no consistent term-to-term rule. The operation must be exactly the same each time.

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