Find missing numbers in sequences

Problem Statement

You are given a list of integers seq that contains exactly one missing term, denoted by the value None. Your goal is to identify the underlying mathematical pattern and return the value of the missing term. The sequence is guaranteed to have at least 4 elements.

The sequence could follow one of these patterns:

1. Arithmetic: Each term increases by a constant d (a_n = a_{n-1} + d).
2. Geometric: Each term is multiplied by a constant r (a_n = a_{n-1} * r).
3. Quadratic: The second difference between terms is constant.
4. Linear Recurrence: Each term is a linear combination of the previous two terms (a_n = c1 * a_{n-1} + c2 * a_{n-2}).

Implement the function: def find_missing_term(seq: List[Optional[int]]) -> int:

Examples

Example 1: Input: [2, 4, 8, None, 32] Output: 16 Explanation: This is a geometric sequence with ratio 2.

Example 2: Input: [1, 4, 9, None, 25] Output: 16 Explanation: This is a sequence of squares (n^2).

Constraints

• Sequence length: 4 <= len(seq) <= 100.
• Values: Integers between -10000 and 10000.
• The missing term will always be an integer.

Edge Cases

• The None value can appear at the beginning, middle, or end of the list.
• If multiple patterns fit, prioritize the most restrictive one (e.g., Arithmetic over Recurrence).