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Find the missing number in the series: 10, 15, 25, 45, ?
75
80
85
90
85
Observe the differences between consecutive terms; they follow a geometric progression of powers of two multiplied by five (5, 10, 20, 40).
Observe the differences between consecutive terms; they follow a geometric progression of powers of two multiplied by five (5, 10, 20, 40).
Analyze consecutive differences
Calculate the difference between each consecutive term: 15 - 10 = 5; 25 - 15 = 10; 45 - 25 = 20.
Identify the pattern
The differences are 5, 10, 20. Each difference is double the previous one (5 * 2 = 10, 10 * 2 = 20). Following this, the next difference must be 20 * 2 = 40.
Calculate the missing number
Add the next calculated difference to the last term in the series: 45 + 40 = 85.
A: 75 is incorrect because it corresponds to adding only 30 instead of 40; B: 80 is incorrect because it corresponds to adding 35; D: 90 is incorrect because it results from adding 45 instead of 40.
C is correct because the series follows a pattern of adding doubling differences (5, 10, 20, 40), where 45 + 40 equals 85.
When the differences between numbers in a series increase rapidly, always check if the differences themselves form a geometric progression or involve powers of 2.
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