Is there a rule to the following sequence? If so, then what is it?
768 , 192 , 48 , 12 , 3
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Is there a rule to the following sequence? If so, then what is it?
768 , 192 , 48 , 12 , 3
Let's analyze the sequence: .
First, observe the relationship between consecutive terms by dividing one term by the previous term:
Each division yields the same factor: .
This indicates a consistent operation of dividing by between the terms. Thus, the rule in the sequence is to divide the current term by to obtain the next term.
Therefore, this sequence follows the rule of dividing each number by to get the next number.
Thus, the correct choice that corresponds to this pattern is:
Yes, multiply by 4.
Is there a term-to-term rule for the sequence below?
18 , 22 , 26 , 30
The question asks for the rule, and 'multiply by 4' means you multiply the current term by 4 to get the previous term. Since , this works backward through the sequence!
Calculate the ratio between consecutive terms. If all ratios are the same (like here), it's geometric! The common ratio can be a fraction, whole number, or even negative.
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.
Absolutely! If the common ratio is greater than 1 (like 2 or 3), the sequence increases. If it's between 0 and 1 (like ), the sequence decreases like this one.
Divide the last term by 4: . The pattern continues with the same rule!
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