To write a recursive formula for the sequence, we first need to analyze the sequence provided. Since you haven't specified the sequence, I'll explain how a recursive formula works and provide an example for a general sequence.

General Structure of a Recursive Formula:

A recursive formula defines each term of a sequence using the preceding term(s). It typically consists of:

1. Initial term(s): This is the base case, where the first term (or the first few terms) is explicitly defined.
2. Recursive relation: This shows how to calculate the next term using the previous term(s).

Example:

For the sequence: $2, 4, 8, 16, \ldots$ (doubles each time):

1. Initial term: $a_1 = 2$
2. Recursive relation: $a_n = 2 \cdot a_{n-1}$, where $n > 1$.

Hence, the recursive formula is: $a_1 = 2,\quad a_n = 2 \cdot a_{n-1},\; n > 1$

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If you have a specific sequence in mind, feel free to provide it. I’ll analyze and derive the recursive formula for you.

Would you like to clarify or ask about the sequence? Below are some questions for further exploration:

1. What is the sequence you want to write the formula for?
2. Are you looking for an arithmetic, geometric, or another type of sequence?
3. Do you need help identifying patterns in the sequence you have?
4. Would you like a visual representation of the sequence or formula?
5. Should the formula include additional constraints (e.g., negative indices)?

Tip: When working with sequences, always verify at least the first few terms to ensure the recursive formula matches the given sequence.