Introduction / Context:
In quantitative aptitude number-series questions, the goal is to uncover the hidden rule that generates each term. Many sequences are built from repeating difference patterns or interleaved mini-sequences. Here, we identify the pattern and predict the next two terms reliably.
Given Data / Assumptions:
- Sequence provided: 17, 17, 34, 20, 20, 31, 23
- We must determine the next two numbers (positions 8 and 9).
- Exactly one pattern should be consistent with all prior terms.
Concept / Approach:
Inspect consecutive differences. If those differences themselves show a repeating or steadily changing pattern, project that pattern forward to get the missing terms. Sometimes sequences use grouped patterns such as triplets that repeat with changing magnitudes.
Step-by-Step Solution:
List differences between consecutive terms:17 → 17 = 017 → 34 = +1734 → 20 = −1420 → 20 = 020 → 31 = +1131 → 23 = −8We observe pairs of triplets repeating the structure [0, +X, −(X−3)], where X decreases by 6 each time: first X = 17, then X = 11.Thus, the next triplet should be [0, +5, −2] because the next X would be 5 (17 → 11 → 5 decreases by 6 each stage).Starting from the last value 23, add the first item of the next triplet (0): 23 + 0 = 23.Then add the second item (+5): 23 + 5 = 28.Therefore, the next two terms are 23 and 28.
Verification / Alternative check:
Grouping into three-term blocks: [17, 17, 34, 20] has differences 0, +17, −14; [20, 20, 31, 23] has 0, +11, −8. Continuing gives [23, 23, 28, 26] if extended further, which matches the projected [0, +5, −2] structure.
Why Other Options Are Wrong:
26 23: Ignores the required 0 then +5 structure.34 20 / 23 33 / 27 28: Each breaks the established grouped-difference rule.
Common Pitfalls:
Treating the series as simple arithmetic progression; failing to notice the repeating 0 step and decreasing positive difference by 6 each cycle.
Final Answer:
23 28
Discussion & Comments