The cycling operations (-1, +2, x3, /4) aren't hard to spot once you check a few differences, but I fumbled the recurrence notation because I kept second-guessing whether to index from 0 or 1.
First, look for patterns in the differences or ratios between consecutive terms, and consider alternating subsequences. Once a rule is hypothesized, test it against the given terms and then formalize it as a recurrence relation, using it to compute the next terms.
Pro tip: In interviews, clearly state your assumptions and walk through your reasoning step-by-step; even if you don't find the exact rule, demonstrating a structured approach and adaptability impresses interviewers.
Calculate the differences between consecutive terms and the ratios to see if they follow a simple pattern. Also check if the sequence alternates between two different operations.
Notice that the sequence might consist of two interleaved subsequences: one for odd positions and one for even positions. Analyze each subsequence separately for patterns.
Based on the patterns, propose a rule that generates the sequence. For example, the rule might involve subtracting 1, adding 2, multiplying by 3, etc., in a repeating cycle.
Apply your hypothesized rule to the given terms to ensure it produces the correct sequence. If it fails, adjust your hypothesis and test again.
Write the recurrence relation formally, specifying how each term depends on previous terms. Then use it to calculate the next several terms.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.