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What should come in place of the question mark (?) in the given series? 6, 15, 34, 63, 102, ?
105
113
151
131
151
Calculate the differences between consecutive terms to find a secondary arithmetic progression increasing by 10 (9, 19, 29, 39, 49).
Calculate the differences between consecutive terms to find a secondary arithmetic progression increasing by 10 (9, 19, 29, 39, 49).
Analyze consecutive differences
Find the difference between each pair: 15-6 = 9; 34-15 = 19; 63-34 = 29; 102-63 = 39.
Identify the logic in differences
The differences are 9, 19, 29, 39. These form an arithmetic progression where each difference increases by 10.
Calculate the final term
Following the pattern, the next difference must be 39 + 10 = 49. Adding this to the last term: 102 + 49 = 151.
A: 105 is incorrect because it ignores the accelerating difference pattern. B: 113 is incorrect as it fails to reach the required sum. D: 131 is incorrect because it underestimates the increment needed after 39.
C is correct because the series follows a pattern of adding consecutive multiples of 10 to the differences, resulting in 102 + 49 = 151.
If the first level of differences does not yield a constant, always calculate the second level of differences; in competitive exams, 90% of series problems are solved within two levels.
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