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Which of the following options should come in place of the question mark (?) in the given series to make it logically complete? 274, 252, 282, 260, 290, 268,?
272
280
284
298
298
Observe the alternating difference pattern: -22, +30, -22, +30, -22, +30.
Observe the alternating difference pattern: -22, +30, -22, +30, -22, +30.
Analyze the pattern between consecutive terms
274 to 252 is -22. 252 to 282 is +30. 282 to 260 is -22. 260 to 290 is +30. 290 to 268 is -22.
Determine the next term
Following the alternating pattern of -22 followed by +30, the next operation after -22 is +30. Thus, 268 + 30 = 298.
A: 272 is incorrect as it does not follow the +30 addition rule. B: 280 is incorrect as it does not follow the +30 addition rule. C: 284 is incorrect as it does not follow the +30 addition rule.
D is correct because the series follows an alternating pattern of subtracting 22 and adding 30, so 268 + 30 results in 298.
For alternating series, always test the arithmetic difference between alternate terms first; if that fails, check consecutive steps for consistent patterns like the one shown here.
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