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Examoogle • User • info@examoogle.com • EE-2024-8821
Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked
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Find the missing number in the series: 10, 12, 16, 24, 40,?
56
64
72
80
72
Observe the differences between consecutive terms; they form a simple geometric progression of powers of 2 (2, 4, 8, 16, 32).
Observe the differences between consecutive terms; they form a simple geometric progression of powers of 2 (2, 4, 8, 16, 32).
Analyze the difference between terms
Calculate the difference between consecutive terms: 12-10=2, 16-12=4, 24-16=8, 40-24=16.
Identify the pattern
The differences are 2, 4, 8, 16, which follow the pattern 2¹, 2², 2³, 2⁴. The next difference must be 2⁵, which is 32.
Calculate the final term
Add the next difference to the last known term: 40 + 32 = 72.
A: 56 is incorrect as it implies a difference of 16 (40+16), which repeats the previous step. B: 64 is incorrect as it suggests an addition of 24, which does not follow the geometric progression. D: 80 is incorrect as it suggests an addition of 40, which does not fit the doubling difference logic.
C is correct because the series follows a pattern of adding successive powers of 2 (2, 4, 8, 16, 32) to the previous term, leading to 40 + 32 = 72.
In any number series, if the numbers grow rapidly, always check the difference of the differences first; if that pattern is a multiplication of 2, you have likely solved the problem.