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To find the recursive formula for the sequence \( 16, 8, 4, \dots \), let’s analyze the pattern in the sequence:

### Observing the Pattern
- The sequence starts at 16, then each subsequent term halves the previous term:
  - \( 16, 8, 4, \dots \)
  - This means each term is multiplied by \( \frac{1}{2} \) to get the next term.

### Recursive Formula
1. The first term \( a_1 \) is:
   \[
   a_1 = 16
   \]
2. The recursive relationship for \( a_n \) in terms of the previous term \( a_{n-1} \) is:
   \[
   a_n = \frac{1}{2} \cdot a_{n-1}
   \]

### Solution
So, the recursive formula can be written as:
- \( a_1 = 16 \)
- \( a_n = \frac{1}{2} a_{n-1} \) for \( n > 1 \)

Would you like further explanation on this process or have any questions?

Here are 5 related questions you might find useful:
1. What is a general formula (non-recursive) for the terms of this sequence?
2. How would the recursive formula change if the sequence was \( 16, 4, 1, \dots \)?
3. Can you create a recursive formula if the sequence were an arithmetic sequence instead?
4. How can you determine if a sequence is geometric or arithmetic?
5. What happens to the recursive formula if the common ratio changes?

**Tip:** Recursive formulas are particularly useful for sequences with a regular pattern, like geometric or arithmetic progressions.

Write a recursive formula for a_n, the nth term of the sequence 16, 8, 4, ....

Learn how to write a recursive formula for the geometric sequence with terms 16, 8, 4, .... This solution provides a step-by-step explanation of identifying a recursive relationship for geometric sequences, suitable for Grades 9-10.

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