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Find the missing number in the series: 2, 6, 12, 20, ?
28
30
32
34
30
Identify the difference between consecutive numbers: they increase by +4, +6, +8, so the next increment must be +10.
Identify the difference between consecutive numbers: they increase by +4, +6, +8, so the next increment must be +10.
Analyze Differences
Calculate the difference between consecutive terms: 6 - 2 = 4, 12 - 6 = 6, 20 - 12 = 8. The differences form a sequence of even numbers: 4, 6, 8.
Predict Next Term
Following the pattern of increasing even numbers, the next difference must be 8 + 2 = 10. Adding this to the last term, 20 + 10 = 30.
Alternative Method (Squares Pattern)
The series follows the formula n squared + n. For n=1: 1+1=2, n=2: 4+2=6, n=3: 9+3=12, n=4: 16+4=20. Thus, for n=5: 25+5=30.
A: 28 is incorrect as it implies an increment of only 8, not 10. C: 32 is incorrect as it implies an increment of 12. D: 34 is incorrect as it follows no logical step-pattern from the sequence.
B is correct because the series follows an arithmetic progression of differences (4, 6, 8, 10), making the next number 20 + 10 = 30.
If the first differences don't show a clear pattern, always calculate the 'second difference' (difference of the differences) to find hidden quadratic relations.
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