Took me a beat to see this wasn't just a standard arithmetic or geometric thing.
Start by examining the differences and ratios between consecutive terms to identify the recurrence. Since the sequence grows rapidly, test multiplicative patterns involving previous terms, possibly with alternating operations. Verify the pattern by checking consistency across all known terms and then compute the missing value.
Pro tip: When a sequence grows rapidly, consider that the recurrence might involve multiplying by an increasing factor or combining previous terms. At Optiver, interviewers value clear, logical reasoning over quick answers, so verbalize your thought process as you test hypotheses.
Calculate the differences and ratios between consecutive terms to see if a simple arithmetic or geometric pattern exists. This initial check helps rule out straightforward patterns.
Since the growth is rapid, focus on multiplicative relationships. Test if each term is derived from the previous term(s) by multiplication, possibly with addition or subtraction.
Consider that the recurrence might alternate between two operations, such as multiply by a and add b, or multiply by increasing factors. Check if the pattern holds for all known terms.
Once a candidate pattern is found, verify it against all given terms. Then apply the pattern to find the missing term and check that the next term (396) is consistent.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.