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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? 36, 72, 45, 90, 63, 126,?
95
99
106
83
99
Observe that the series consists of two alternating operations applied to every consecutive pair: multiply by 2 (e.g., 36 * 2 = 72) and then subtract 27 (e.g., 72 - 27 = 45).
Observe that the series consists of two alternating operations applied to every consecutive pair: multiply by 2 (e.g., 36 * 2 = 72) and then subtract 27 (e.g., 72 - 27 = 45).
Analyze the pattern
Looking at the series 36, 72, 45, 90, 63, 126,?, we can see a clear pattern of pairs: (36, 72), (45, 90), (63, 126). Each second number is exactly double the previous number (36 * 2 = 72; 45 * 2 = 90; 63 * 2 = 126).
Analyze the transitions between pairs
Look at the transition from the end of one pair to the start of the next: 72 to 45 (72 - 27 = 45) and 90 to 63 (90 - 27 = 63). Thus, the next term after 126 should be 126 - 27 = 99.
A: 95 is incorrect as the calculated result is 99. C: 106 is incorrect because it does not follow the -27 subtraction rule from the previous term 126. D: 83 is incorrect as it does not follow the derived arithmetic progression.
B is correct because the series follows a pattern of multiplying by 2 followed by subtracting 27, and 126 minus 27 equals 99.
In competitive exams, always check for alternating operations or grouped pairs when you see numbers doubling or halving suddenly in a sequence.
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