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Find the missing number: 2, 6, 12, 20, 30, ?
42
40
36
44
42
Recognize the standard product pattern n(n+1) or check the increasing difference sequence (+4, +6, +8, +10, +12).
Recognize the standard product pattern n(n+1) or check the increasing difference sequence (+4, +6, +8, +10, +12).
Analyze Consecutive Differences
Find the difference between consecutive terms: 6 - 2 = 4, 12 - 6 = 6, 20 - 12 = 8, and 30 - 20 = 10. The differences increase by 2 each time.
Calculate Missing Term
The next difference in sequence after 10 is 10 + 2 = 12. Add this difference to the last term: 30 + 12 = 42.
B: 40 is incorrect because it comes from a wrong difference step. C: 36 is incorrect as it corresponds to earlier increments. D: 44 is incorrect because it assumes an incorrect difference of 14.
A is correct because the sequence follows an increasing difference pattern of consecutive even numbers (+4, +6, +8, +10, +12), making the missing term 30 + 12 = 42.
Always check both single differences and double differences if the pattern isn't immediately obvious.