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Find the missing term in the sequence: 2, 6, 12, 20, 30, ?
40
42
44
46
42
Observe the differences between consecutive terms: they form an arithmetic progression of even numbers (+4, +6, +8, +10).
Observe the differences between consecutive terms: they form an arithmetic progression of even numbers (+4, +6, +8, +10).
Analyze the differences between terms
Calculate the difference between consecutive terms: (6-2)=4, (12-6)=6, (20-12)=8, (30-20)=10.
Identify the pattern and predict the next term
The differences are consecutive even numbers (4, 6, 8, 10). Following this logic, the next difference must be 12. Adding 12 to the last term (30), we get 30 + 12 = 42.
A: 40 is incorrect because the difference 10 is followed by 12, not 10; C: 44 is incorrect as it results from adding 14; D: 46 is incorrect as it results from adding 16.
B is correct because the sequence follows a pattern of adding consecutive even numbers (+4, +6, +8, +10, +12), resulting in 30 + 12 = 42.
For number series, if the difference between terms is not constant, calculate the 'difference of the differences' to reveal the underlying quadratic or arithmetic pattern.
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