The sequence $4, 8, 16, 32, \dots$ appears to follow a geometric progression where each term is obtained by multiplying the previous term by 2.

Recursive Formula

To express this sequence recursively:

1. Base case: Define the first term: $a_1 = 4$
2. Recursive step: Define how each subsequent term relates to the previous one: $a_n = 2 \cdot a_{n-1}, \quad \text{for } n \geq 2$

Final Recursive Formula:

$a_1 = 4, \quad a_n = 2 \cdot a_{n-1}, \quad n \geq 2$

This defines the sequence where each term doubles the preceding one.

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Would you like details about how this relates to general sequences or help with similar sequences? Here are five related questions to explore further:

1. What is the explicit formula for this sequence?
2. How does the growth of a geometric sequence compare to an arithmetic sequence?
3. Can you derive the sum of the first $n$ terms of this geometric sequence?
4. What are the applications of geometric sequences in real-world problems?
5. How would you modify the recursive formula if the sequence started at 6 instead of 4?

Tip: Recursive formulas are best for understanding sequential relationships, but explicit formulas are easier for finding large terms directly.