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Find the next number in the series: 2, 6, 12, 20, 30,?
40
42
44
46
42
Identify the difference between consecutive terms; this series forms an arithmetic progression of even numbers (4, 6, 8, 10, 12).
Identify the difference between consecutive terms; this series forms an arithmetic progression of even numbers (4, 6, 8, 10, 12).
Analyze the difference between terms
Calculate the difference between each consecutive term: 6-2=4, 12-6=6, 20-12=8, 30-20=10.
Identify the pattern
The differences are 4, 6, 8, 10, which are consecutive even numbers increasing by 2.
Calculate the final term
The next difference must be 12. Adding this to the last known term: 30 + 12 = 42.
A: 40 is incorrect as it only adds 10, repeating the previous difference instead of incrementing. C: 44 is incorrect as it implies a difference of 14, skipping the required step of 12. D: 46 is incorrect as it implies a difference of 16, which does not follow the established +2 increment pattern.
B is correct because the series follows a pattern of adding consecutive even numbers (4, 6, 8, 10, 12) to the previous term, resulting in 30 + 12 = 42.
For number series, if the difference between terms increases linearly, always check the double difference (the difference of the differences) to confirm the pattern quickly.