Difficulty: Easy
Correct Answer: 996
Explanation:
Introduction / Context:
This series alternates between decreasing and increasing values. Frequently, such patterns are created by interleaving two simple sequences, one on the odd positions and one on the even positions. Identifying these two subsequences is the key to finding the next term.
Given Data / Assumptions:
Concept / Approach:
We extract the numbers in odd positions and even positions separately. If each subsequence has its own constant difference pattern, then we can extend the appropriate subsequence to find the missing term in the combined series.
Step-by-Step Solution:
Step 1: Write the odd position terms: 1st 999, 3rd 998, 5th 997, 7th ?.Step 2: This odd subsequence clearly decreases by 1 each time: 999, 998, 997, 996.Step 3: Therefore the 7th term in the series, belonging to the odd subsequence, must be 996.Step 4: For completeness, list even position terms: 2nd 990, 4th 991, 6th 992. This subsequence increases by 1 each time, confirming a neat opposing pattern.
Verification / Alternative check:
Recombine the two subsequences: 999 (odd), 990 (even), 998 (odd), 991 (even), 997 (odd), 992 (even), 996 (odd). The odd positions form a strictly decreasing sequence and the even positions form a strictly increasing sequence, both by steps of 1. This confirms that 996 is the only correct continuation for the series.
Why Other Options Are Wrong:
Numbers like 1000 or 1001 would break the decreasing pattern in the odd positions. A value like 999 would repeat a previous odd term, and 993 belongs more naturally to the even subsequence pattern and not to the odd one at this position.
Common Pitfalls:
Some test takers try to see a single pattern through the entire list without separating odd and even positions, which can be confusing. Recognising that the series may be interleaving two simpler progressions simplifies the reasoning dramatically.
Final Answer:
The number that correctly continues the pattern is 996.
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