Start by examining the sequence for simple patterns: differences, ratios, or operations. Notice each term is double the previous, so the next term is 48. Then discuss the pattern's properties and potential edge cases to show depth.
Pro tip: At Optiver, interviewers value clear, logical reasoning over just the answer. Verbalize your thought process step-by-step, and mention that such sequences can have multiple valid continuations depending on the rule, but the simplest is geometric doubling.
Look at the relationship between consecutive terms. Check differences (3, 6, 12, 24) and ratios (2, 2, 2).
Recognize that each term is multiplied by 2 to get the next term. This is a geometric sequence with common ratio 2.
Multiply the last term (24) by 2 to get the next term: 48.
Check that the rule holds for all given terms. Mention that other patterns (e.g., adding increasing powers of 2) could also fit, but the simplest is doubling.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
First, identify the pattern in the sequence. Notice that the numbers are prime numbers, so the next number is the next prime after 11, which is 13. Then, consider alternative patterns and explain why the prime number pattern is the most plausible.
Pro tip: At Optiver, interviewers value clear reasoning and the ability to consider multiple hypotheses. Even if you recognize the pattern quickly, briefly mention other possibilities and why they are less likely, demonstrating thoroughness.
List the given numbers: 2, 3, 5, 7, 11. Look for common properties such as parity, divisibility, or known sequences.
Recognize that all numbers are prime. Verify that each number has no divisors other than 1 and itself.
Find the next prime number after 11. Check 12 (not prime), 13 (prime), so the next number is 13.
Briefly explore other possible patterns (e.g., differences, Fibonacci-like) and explain why they don't fit as well as the prime sequence.
Conclude that the next number is 13, and summarize the reasoning that the sequence consists of consecutive prime numbers.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
First, identify the pattern by checking differences between consecutive terms: 3, 5, 7, which are consecutive odd numbers. Then, recognize that the sequence consists of perfect squares (1^2, 2^2, 3^2, 4^2), so the next term is 5^2 = 25. Finally, articulate your reasoning clearly and consider alternative patterns to demonstrate thoroughness.
Pro tip: At Optiver, interviewers value not just the correct answer but also your ability to explain your thought process and handle ambiguity. Mention that while the pattern is likely perfect squares, you would verify with additional terms if available, showing scientific rigor.
Look at the given numbers: 1, 4, 9, 16. Notice they are all perfect squares of consecutive integers starting from 1.
Confirm the pattern: 1=1^2, 4=2^2, 9=3^2, 16=4^2. The next term should be 5^2.
Calculate 5^2 = 25. This is the most straightforward answer based on the identified pattern.
Check if other patterns fit, such as differences (3,5,7, next difference 9 gives 25) or polynomial fits. This shows robustness in reasoning.
State the answer clearly (25) and explain the reasoning, including why you chose that pattern over others.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
The differences are 1, 2, 3, 4, 5 so the next difference is 6, giving you 22.
First, compute the differences between consecutive terms to see if a simple pattern emerges. If the differences are not constant, look at second differences or other common patterns (e.g., squares, primes). If no pattern is immediately obvious, systematically test common sequences and be prepared to discuss your reasoning and fallback strategies.
Pro tip: At Optiver, they value not just the answer but your thought process and how you handle uncertainty. Verbalize your reasoning clearly and if you're stuck, propose a reasonable fallback like assuming a polynomial pattern or asking clarifying questions.
Calculate the differences between consecutive terms: 2-1=1, 4-2=2, 7-4=3, 11-7=4, 16-11=5. The differences are 1, 2, 3, 4, 5, so the next difference is likely 6.
The differences increase by 1 each time, indicating a quadratic sequence. The next term is 16 + 6 = 22.
Check second differences: 2-1=1, 3-2=1, 4-3=1, 5-4=1. Constant second difference confirms a quadratic pattern.
If no pattern is apparent, try common sequences (Fibonacci, primes, squares, etc.), consider polynomial fits, or ask if there are additional constraints. State your assumptions and reasoning.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.