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What should come in place of the question mark in the following series: 2, 6, 12, 20, 30, ?
40
42
44
46
42
Identify the difference between consecutive terms; this is a square-based sequence where n squared plus n or n times n plus 1 produces the terms.
Identify the difference between consecutive terms; this is a square-based sequence where n squared plus n or n times n plus 1 produces the terms.
Analyze the pattern of differences
Calculate the difference between consecutive numbers: 6-2=4, 12-6=6, 20-12=8, 30-20=10. The differences are 4, 6, 8, 10, which are consecutive even numbers increasing by 2.
Determine the next difference
Following the pattern of even numbers (4, 6, 8, 10), the next increment must be 12.
Calculate the final term
Add the next difference to the last known term: 30 + 12 = 42.
A: 40 is incorrect as it only adds 10 to the previous term, failing the increment pattern. C: 44 is incorrect as it assumes an increment of 14, which breaks the +2 difference pattern. D: 46 is incorrect as it assumes an increment of 16, inconsistent with the established progression.
B is correct because the series follows an increasing difference pattern of +4, +6, +8, +10, and finally +12, resulting in 30 + 12 = 42.
If a series is not arithmetic or geometric, always check the difference of differences first. Many competitive exam questions use n┬▓тБ║тБ┐ or n┬▓тБ╗тБ┐ patterns.
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