Each term doubles the previous one and subtracts 1, so 33 times 2 minus 1 gives 65.
First, identify the pattern by examining differences between consecutive terms: 1, 2, 4, 8, 16, which are powers of 2. Then, use this to predict the next difference and compute the next term. Finally, explain the reasoning clearly and consider alternative patterns.
Pro tip: After finding the pattern, briefly mention that you'd validate it with more terms or consider if other patterns exist, showing thoroughness. Also, relate it to how you'd approach pattern recognition in data science, such as time series analysis.
Write down the given numbers: 2, 3, 5, 9, 17, 33. Look for simple relationships between consecutive terms.
Compute the differences: 3-2=1, 5-3=2, 9-5=4, 17-9=8, 33-17=16. Notice that the differences are powers of 2: 2^0, 2^1, 2^2, 2^3, 2^4.
The differences double each time, so the next difference should be 32 (2^5). Alternatively, each term is previous term plus a power of 2, or each term is 2*previous term - 1.
Add the next difference (32) to the last term (33) to get 65. Verify using the alternative pattern: 2*33 - 1 = 65.
Clearly state the pattern and how you arrived at the answer. Mention that you checked multiple perspectives to ensure consistency.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Two interleaved sequences running in parallel: one doubles each step (1, 2, 4, 8...) and the other does the same but offset (4, 8, 16, 32...).
First, scan the sequence for alternating patterns or operations. Notice that odd-positioned terms (1,2,4,8) double each time, while even-positioned terms (4,8,16,32) also double. Then extend each subsequence to find the next two values.
Pro tip: Verbalize your reasoning step-by-step, as interviewers value clear thought process over just the answer. Also, briefly mention that such patterns can be modeled as two interleaved geometric sequences, showing your data science mindset.
Write down the given numbers and look for simple relationships like addition, multiplication, or alternation.
Separate the sequence into odd and even positions. Check if each subsequence follows a consistent rule.
For odd positions: 1,2,4,8 → multiply by 2 each time. For even positions: 4,8,16,32 → multiply by 2 each time.
The next odd-position term after 8 is 16; the next even-position term after 32 is 64.
Check that the pattern holds for all given terms and state the next two values clearly: 16 and 64.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Each term is 2 to the power of n minus 1, so the next is 63.
Start by examining the differences between consecutive terms to identify the pattern, then generalize it to find the next term. Clearly state the rule and verify it with the given sequence before providing the answer.
Pro tip: After finding the answer, mention that this is a geometric progression with ratio 2 plus 1, and relate it to binary representation or exponential growth, which is common in data science contexts like algorithm complexity or growth models.
Calculate the differences between consecutive terms: 3-1=2, 7-3=4, 15-7=8, 31-15=16. Notice that the differences double each time.
Express the pattern as a recurrence relation: each term is twice the previous term plus 1 (a_n = 2*a_{n-1} + 1). Alternatively, recognize that each term is one less than a power of 2: 1=2^1-1, 3=2^2-1, 7=2^3-1, etc.
Using the recurrence, the next term is 2*31 + 1 = 63. Using the power of 2 pattern, the next term is 2^6 - 1 = 63.
Check that 63 fits the pattern: 63-31=32, which is double the previous difference (16). Also, 63 = 2^6 - 1, continuing the sequence.
Mention that such sequences often appear in algorithm analysis (e.g., number of nodes in a perfect binary tree of height h is 2^{h+1}-1) or in exponential growth models, demonstrating relevance to the role.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Each row sums the first two values to get the third: 7+4=11, 5+9=14, so ?+13=18 means the missing number is 5.
First, identify the pattern within each row by comparing the first two numbers to the third. Then, apply the discovered rule to the third row to find the missing value, and clearly articulate the rule for each row.
Pro tip: After finding the answer, briefly mention how you would validate the pattern with additional data or edge cases, showing a data scientist's rigor.
Look at the first two rows to see how the third number is derived from the first two. For example, in row 1: 7 + 4 = 11; in row 2: 5 + 9 = 14.
Notice that in each row, the third number is the sum of the first two numbers. This is a consistent rule across the rows.
Use the rule to find the missing value: ? + 13 = 18, so ? = 5.
State clearly that the rule is: the third number in each row equals the sum of the first two numbers.
Check that the rule holds for all rows, and consider if there are alternative patterns or if the rule could be extended to columns or other structures.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.