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Which of the following options should come in place of the question mark (?) in the given series to make it logically complete? 24, 26, 30, 36, 44,?
54
57
53
51
54
Look at the differences between consecutive terms: 2, 4, 6, 8, 10. The differences increase by 2 each time.
Look at the differences between consecutive terms: 2, 4, 6, 8, 10. The differences increase by 2 each time.
Step 1: Find differences between consecutive terms
26 - 24 = 2, 30 - 26 = 4, 36 - 30 = 6, 44 - 36 = 8.
Step 2: Identify pattern in differences
The differences are consecutive even numbers: 2, 4, 6, 8. Following this pattern, the next difference must be 10.
Step 3: Calculate the missing term
Add 10 to the last given term: 44 + 10 = 54.
B: 57 is incorrect because it does not follow the +10 difference increment. C: 53 is incorrect as it is an odd number and breaks the even increment pattern. D: 51 is incorrect because it yields incorrect differences.
A is correct because the series increases by consecutive even numbers (+2, +4, +6, +8, +10), giving 44 + 10 = 54.
Always check the difference of differences (second difference) if the first difference sequence forms an arithmetic progression.
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