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What should come in place of the question mark (?) in the given series? 28, 29, 27, 30, 26, ?
32
25
31
24
31
Whenever a series oscillates between increasing and decreasing, check for two separate alternating series interleaved within the sequence.
Whenever a series oscillates between increasing and decreasing, check for two separate alternating series interleaved within the sequence.
Analyze the Alternating Series
The given series is 28, 29, 27, 30, 26, ?. We can split this into two interleaved series. Sequence 1 (1st, 3rd, 5th terms): 28, 27, 26 (decreasing by 1). Sequence 2 (2nd, 4th, 6th terms): 29, 30, ? (increasing by 1).
Calculate the Missing Term
Following Sequence 2, the pattern is 29 (+1) = 30, and 30 (+1) = 31. Therefore, the missing term (?) is 31.
A: 32 is incorrect because the pattern for the second sequence is +1, not +2; B: 25 is incorrect because it follows the first sequence pattern (26 - 1), ignoring the alternating requirement; D: 24 is incorrect as it has no logical connection to the arithmetic progression of the second sequence.
C is correct because the series consists of two alternating patterns, where the second sequence increments by 1 (29, 30, 31), identifying 31 as the next term.
If a series is neither purely increasing nor decreasing, always check if it is composed of two or more independent series running in parallel.
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