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Find the missing term in the series: 2, 6, 12, 20, 30, ?
40
42
44
46
42
Observe the differences between consecutive terms (4, 6, 8, 10) which follow an arithmetic progression of +2, or recognize the series as n(n+1) where n starts from 1.
Observe the differences between consecutive terms (4, 6, 8, 10) which follow an arithmetic progression of +2, or recognize the series as n(n+1) where n starts from 1.
Analyze consecutive differences
Find the difference between consecutive terms: 6-2=4, 12-6=6, 20-12=8, 30-20=10. The differences are 4, 6, 8, 10.
Identify the pattern in differences
The differences increase by 2 each time (4, 6, 8, 10). Therefore, the next difference must be 10 + 2 = 12.
Calculate the final term
Add the next difference to the last term of the series: 30 + 12 = 42.
A: 40 is incorrect as it fails to follow the +12 increment; C: 44 is incorrect as it assumes a +14 increment; D: 46 is incorrect as it assumes a +16 increment.
B is correct because the series follows an increasing difference pattern of 4, 6, 8, 10, 12, resulting in 30 + 12 = 42.
For any series, if the first level of differences doesn't show a clear pattern, calculate the second level (difference of differences) which is constant in this case (+2).
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