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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? 351, 380, 413, 450, 491,?
536
530
512
541
536
Calculate the differences between consecutive terms: they follow the pattern of adding consecutive odd numbers starting from 29 (29, 33, 37, 41, 45).
Calculate the differences between consecutive terms: they follow the pattern of adding consecutive odd numbers starting from 29 (29, 33, 37, 41, 45).
Calculate Differences
Find the difference between consecutive terms: 380 - 351 = 29, 413 - 380 = 33, 450 - 413 = 37, 491 - 450 = 41.
Identify Pattern
Observe the differences: 29, 33, 37, 41. These increase by 4 each time (29+4=33, 33+4=37, 37+4=41).
Calculate Final Term
The next difference should be 41 + 4 = 45. Add this to the last term: 491 + 45 = 536.
B: 530 is incorrect as it implies a +39 increment; C: 512 is too small; D: 541 implies a +50 increment which does not fit the +4 step pattern.
A is correct because the series follows a pattern of adding consecutive increments of 29, 33, 37, 41, and 45 to each preceding number.
In any number series, if the numbers are increasing slowly, always check the difference between consecutive terms first as it frequently reveals a simple arithmetic pattern.
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