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What should come in place of the question mark (?) in the given series? 54, 43, 33, 24, 16, ?
9
11
6
8
9
Observe the decreasing differences between consecutive numbers: the subtrahend itself decreases by 1 at each step (11, 10, 9, 8, 7).
Observe the decreasing differences between consecutive numbers: the subtrahend itself decreases by 1 at each step (11, 10, 9, 8, 7).
Analyze the pattern of differences
Calculate the difference between consecutive terms: 54 - 43 = 11; 43 - 33 = 10; 33 - 24 = 9; 24 - 16 = 8.
Determine the next term
The differences are decreasing by 1 (11, 10, 9, 8). Therefore, the next difference must be 8 - 1 = 7. Subtracting 7 from the last term 16 gives: 16 - 7 = 9.
B: 11 is incorrect because it implies an increase or a wrong arithmetic sequence; C: 6 is incorrect as it results from a wrong subtraction pattern; D: 8 is incorrect as it would imply the pattern of subtraction repeats 8 instead of decreasing to 7.
A is correct because the series follows a pattern of subtracting consecutive integers starting from 11, where 16 minus 7 equals 9.
In number series, if the gap between numbers is small, always check the difference of differences first as it usually reveals a linear or constant acceleration pattern.
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