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Find the next term in the series: 2, 6, 12, 20, 30, ?
40
42
44
46
42
Identify the difference between consecutive terms; this series follows the pattern of adding consecutive even numbers (+4, +6, +8, +10, +12) or the square logic (n squared + n).
Identify the difference between consecutive terms; this series follows the pattern of adding consecutive even numbers (+4, +6, +8, +10, +12) or the square logic (n squared + n).
Analyze the differences between terms
Find the difference between consecutive terms: 6-2=4, 12-6=6, 20-12=8, 30-20=10. The difference increases by 2 each time.
Calculate the next term
The next difference should be 10 + 2 = 12. Therefore, the next term is 30 + 12 = 42.
Alternative Square Logic
The series follows the formula n squared + n: (11+1=2), (22+2=6), (33+3=12), (44+4=20), (55+5=30), (66+6=42).
A: 40 is incorrect as it only adds 10 to the previous term, failing the increasing difference pattern. C: 44 is incorrect as it adds 14, skipping the required step of 12. D: 46 is incorrect as it assumes an increment of 16, which does not fit the +2 progression.
B is correct because the series follows an incremental difference pattern starting at 4, increasing by 2 for each subsequent step (4, 6, 8, 10, 12), leading to 30 + 12 = 42.
For any number series, if the numbers grow slowly, always check the difference between terms first. If the differences are not constant, check the differences of the differences.
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