Introduction / Context:
Some sequences use repeated pairs, each pair decreasing by a fixed step. Spotting the “pair then drop” behavior is the fastest route to the next terms, especially in time-pressured exams.
Given Data / Assumptions:
- Sequence: 20, 20, 17, 17, 14, 14, 11
- We must find positions 8 and 9.
- The values appear in repeated pairs that step down by 3.
Concept / Approach:
Identify the repeating pattern: two identical numbers, then the next pair is reduced by 3, and so on. Extend by completing the current pair and then preparing the next pair if needed.
Step-by-Step Solution:
Pairs observed: (20, 20), (17, 17), (14, 14), followed by a single 11 so far.Each new pair is 3 less than the previous: 20 → 17 → 14 → 11 → 8…Since only one 11 is present, the very next term must complete this pair: 11.After completing the pair, the next pair would be 8, 8; but the question asks only for the next two terms, which are 11 and 11.
Verification / Alternative check:
Continuing the pattern beyond the asked range would yield 8, 8, confirming the consistent −3 step across pairs.
Why Other Options Are Wrong:
8 8 / 11 14 / 8 9 / 11 8: They either skip completing the current 11 pair or break the fixed −3 between successive pairs.
Common Pitfalls:
Jumping straight to the next lower pair (8, 8) without first completing the remaining 11 in the current pair.
Final Answer:
11 11
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