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Complete the series: 2, 6, 12, 20, 30, ?
40
42
44
46
42
Identify the pattern either as products of consecutive integers n(n+1) or by checking the second difference which is constant at +2.
Identify the pattern either as products of consecutive integers n(n+1) or by checking the second difference which is constant at +2.
Find the Differences
Calculate the difference between consecutive terms: 6 minus 2 is 4, 12 minus 6 is 6, 20 minus 12 is 8, and 30 minus 20 is 10. The differences are 4, 6, 8, 10, which increase by 2 each time.
Calculate the Missing Term
Following the pattern, the next difference must be 10 plus 2, which is 12. Adding this to the last term gives 30 plus 12 equals 42.
A: 40 is incorrect because it results from adding 10 instead of 12. C: 44 and D: 46 are incorrect calculations that do not fit the established difference pattern.
B is correct because the series follows a difference pattern of consecutive even numbers increasing by 2, yielding 30 + 12 = 42.
When first differences form an arithmetic progression, checking the second difference will immediately reveal the underlying rule.
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