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.