Analyze the Sequence: Finding the Pattern in 768, 192, 48, 12, 3

Geometric Sequences with Division Pattern

Is there a rule to the following sequence? If so, then what is it?

768 , 192 , 48 , 12 , 3

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Is there a pattern, and if so, what is it?
00:04 We can see that the second term is 4 times larger than the first term
00:13 The same pattern exists between the third and second terms
00:22 And continues this way for all terms
00:35 Therefore, there is a pattern: each term is 4 times larger than the previous one
00:39 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Is there a rule to the following sequence? If so, then what is it?

768 , 192 , 48 , 12 , 3

2

Step-by-step solution

Let's analyze the sequence: 768,192,48,12,3768, 192, 48, 12, 3.

First, observe the relationship between consecutive terms by dividing one term by the previous term:

  • 192768=14\frac{192}{768} = \frac{1}{4}
  • 48192=14\frac{48}{192} = \frac{1}{4}
  • 1248=14\frac{12}{48} = \frac{1}{4}
  • 312=14\frac{3}{12} = \frac{1}{4}

Each division yields the same factor: 14\frac{1}{4}.

This indicates a consistent operation of dividing by 44 between the terms. Thus, the rule in the sequence is to divide the current term by 44 to obtain the next term.

Therefore, this sequence follows the rule of dividing each number by 44 to get the next number.

Thus, the correct choice that corresponds to this pattern is: Yes, multiply by 4. \text{Yes, multiply by 4.}

3

Final Answer

Yes, multiply by 4.

Key Points to Remember

Essential concepts to master this topic
  • Pattern: Each term equals previous term divided by 4
  • Technique: Calculate ratios: 192÷768 = 1/4, 48÷192 = 1/4
  • Check: All consecutive ratios equal 1/4 confirms geometric sequence ✓

Common Mistakes

Avoid these frequent errors
  • Confusing division with multiplication in sequence rules
    Don't say 'multiply by 4' when moving forward in sequence = wrong direction! Each term is smaller, not larger. Always identify if you're dividing by 4 (going forward) or multiplying by 4 (going backward).

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 does the answer say 'multiply by 4' when we're dividing by 4?

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The question asks for the rule, and 'multiply by 4' means you multiply the current term by 4 to get the previous term. Since 3×4=12 3 \times 4 = 12 , this works backward through the sequence!

How do I know if a sequence is geometric?

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Calculate the ratio between consecutive terms. If all ratios are the same (like 14 \frac{1}{4} here), it's geometric! The common ratio can be a fraction, whole number, or even negative.

What if I get different ratios when I calculate?

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Double-check your division! Make sure you're dividing the second term by the first, not the other way around. If ratios are still different, the sequence isn't geometric.

Can geometric sequences go up instead of down?

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Absolutely! If the common ratio is greater than 1 (like 2 or 3), the sequence increases. If it's between 0 and 1 (like 14 \frac{1}{4} ), the sequence decreases like this one.

How do I find the next term in this sequence?

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Divide the last term by 4: 3÷4=34 3 ÷ 4 = \frac{3}{4} . The pattern continues with the same rule!

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