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Which of the following options should come in place of the question mark (?) in the given series? 12, 23, 35, 48, 62,?
75
77
79
81
77
Observe the differences between consecutive terms: 11, 12, 13, 14... the next difference must be 15.
Observe the differences between consecutive terms: 11, 12, 13, 14... the next difference must be 15.
Analyze the pattern
Calculate the difference between consecutive numbers: 23 - 12 = 11, 35 - 23 = 12, 48 - 35 = 13, 62 - 48 = 14.
Apply the pattern
The differences are increasing by 1 each time (11, 12, 13, 14). Therefore, the next difference must be 15. Adding 15 to the last term: 62 + 15 = 77.
A: 75 is wrong because it corresponds to adding 13 instead of 15; C: 79 is wrong because it corresponds to adding 17; D: 81 is wrong because it corresponds to adding 19.
B is correct because the series follows a pattern of increasing differences (11, 12, 13, 14, 15), and 62 + 15 equals 77.
If the series grows slowly, always check the difference of differences; if the difference between terms is consistent, it's a simple arithmetic progression.