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What should come in place of the question mark (?) in the given series? 25, 30, 40, 55, 75, ?
95
100
90
105
100
Observe the differences between consecutive terms; they follow an arithmetic progression of multiples of 5 (5, 10, 15, 20...).
Observe the differences between consecutive terms; they follow an arithmetic progression of multiples of 5 (5, 10, 15, 20...).
Analyze consecutive differences
Calculate the difference between each pair: 30 - 25 = 5; 40 - 30 = 10; 55 - 40 = 15; 75 - 55 = 20.
Identify the pattern and calculate the next term
The differences are increasing by 5 (5, 10, 15, 20). Following this logic, the next difference must be 20 + 5 = 25. Therefore, the missing term is 75 + 25 = 100.
A: 95 is incorrect as it implies a constant difference of 20, ignoring the increasing sequence. C: 90 is incorrect as it results from an inconsistent jump of 15. D: 105 is incorrect as it results from an arbitrary jump of 30.
B is correct because the series follows a pattern of adding multiples of 5 (5, 10, 15, 20, 25) to each preceding term, leading to 75 + 25 = 100.
When a series increases at an increasing rate, always find the 'difference of the differences' (second-order difference) to reveal the underlying growth rule.
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