Series Completion - Question and answers

I've implemented basic checks for simple arithmetic and geometric progressions, but my function fails when dealing with patterns like Fibonacci, alternating sequences, or those with nested rules. For example, if the series is 2, 4, 8, 16, it works fine, but for 1, 1, 2, 3, 5 or 1, 3, 2, 4, 3, it doesn't detect the correct rule. I'm working with limited input terms (usually 4-5) and need a solution that's efficient and accurate for educational purposes. I've tried using if-else chains, but it feels messy and not scalable.