a sequence starts 1/2 , 1/4 , 1/8 give a rule that the sequence could follow , follow that rule to write 3 terms in the sequence 

The sequence you provided is: \( \frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \dots \).

This sequence can be described by the following rule: **Each term is half of the previous term**. 

In mathematical terms, the \(n\)-th term of the sequence \(a_n\) can be expressed as:

\[
a_n = \frac{1}{2^n}
\]

Using this rule, let's find the next three terms:

1. The 4th term: \( a_4 = \frac{1}{2^4} = \frac{1}{16} \)
2. The 5th term: \( a_5 = \frac{1}{2^5} = \frac{1}{32} \)
3. The 6th term: \( a_6 = \frac{1}{2^6} = \frac{1}{64} \)

So, the next three terms in the sequence are \( \frac{1}{16}, \frac{1}{32}, \frac{1}{64} \).

Would you like more details, or do you have any questions?

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Here are 5 related questions:

1. What is the 10th term in this sequence?
2. Can this sequence be classified as a geometric sequence? Why or why not?
3. How would you find the sum of the first \( n \) terms of this sequence?
4. What is the common ratio of this sequence?
5. If the first term of a similar sequence is \( \frac{3}{4} \) and follows the same rule, what would the first three terms be?

**Tip:** In geometric sequences, the common ratio is the factor you multiply by to get from one term to the next.

Explore how to generate terms in a geometric sequence starting with 1/2, 1/4, 1/8. Learn the rule that each term is half of the previous term, and find the next three terms in the sequence. Discover related questions and detailed explanations. Perfect for high school students studying sequences and series.

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