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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? 78, 124, 152, 198, 226, 272,?
300
286
320
294
300
Identify the alternating addition pattern: the difference between consecutive numbers follows a repeating sequence of +46, +28, +46, +28, +46. The next step is +28.
Identify the alternating addition pattern: the difference between consecutive numbers follows a repeating sequence of +46, +28, +46, +28, +46. The next step is +28.
Analyze the difference between terms
124 - 78 = 46; 152 - 124 = 28; 198 - 152 = 46; 226 - 198 = 28; 272 - 226 = 46.
Determine the pattern
The differences alternate between +46 and +28. Following the sequence 46, 28, 46, 28, 46, the next difference must be 28.
Calculate the final term
Add 28 to the last term: 272 + 28 = 300.
B: 286 is incorrect as the pattern is +28; C: 320 is incorrect because 272+48 would be wrong; D: 294 is incorrect because 272+22 is wrong.
A is correct because the series follows an alternating addition pattern of +46 and +28, and 272 + 28 = 300.
In arithmetic series with fluctuating differences, always write down the difference between consecutive terms to reveal simple repeating cycles.
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