a sequence starts 1/2, 1/4, 1/8,... a. Give a rule tat the sequence could follow.

The sequence you provided is:

\[
\frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \ldots
\]

To identify a rule that this sequence could follow, we observe that each term is half of the previous term.

### Rule for the Sequence:

Each term in the sequence is obtained by multiplying the previous term by \(\frac{1}{2}\).

Alternatively, you can express this sequence using the formula for the \(n\)th term:

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

where \(n\) starts from 1. 

Thus:

- \(a_1 = \frac{1}{2^1} = \frac{1}{2}\)
- \(a_2 = \frac{1}{2^2} = \frac{1}{4}\)
- \(a_3 = \frac{1}{2^3} = \frac{1}{8}\)
- And so on...

Would you like any more details or explanations?

Here are five related questions:

1. What type of sequence is this, arithmetic or geometric?
2. How would you find the 10th term in this sequence?
3. What happens to the terms as \(n\) increases indefinitely?
4. Can you find the sum of the infinite series of this sequence?
5. How would the rule change if the sequence started with \(\frac{3}{2}\) instead of \(\frac{1}{2}\)?

**Tip:** This sequence is an example of a geometric sequence, where each term is obtained by multiplying the previous term by a constant factor, known as the common ratio.

Explore the geometric sequence 1/2, 1/4, 1/8, ... and understand its pattern. Learn how to find the nth term and identify the common ratio. Suitable for Grades 7-9 students studying sequences and geometric patterns.

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