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What should come in place of the question mark (?) in the given series? 180 131 90 57 32 ?
22
20
17
15
15
Calculate the difference between consecutive terms. Observe the pattern of subtracting consecutive odd numbers starting from 49.
Calculate the difference between consecutive terms. Observe the pattern of subtracting consecutive odd numbers starting from 49.
Calculate differences between consecutive terms
180 - 131 = 49; 131 - 90 = 41; 90 - 57 = 33; 57 - 32 = 25.
Identify the pattern of the differences
The differences are 49, 41, 33, 25. Notice the gap between these differences is constant: 49 - 8 = 41; 41 - 8 = 33; 33 - 8 = 25; 25 - 8 = 17.
Apply the final subtraction
The next difference must be 17. Subtracting 17 from the last term 32 gives 32 - 17 = 15.
A: 22 is incorrect because it is the result of 32-10, which doesn't fit the decreasing 8 pattern. B: 20 is incorrect because it is the result of 32-12, failing to maintain the constant subtraction gap. C: 17 is incorrect because it is the subtraction value itself, not the resulting series term.
D is correct because the series follows a pattern of subtracting consecutive terms by a decreasing gap of 8 (49, 41, 33, 25, 17), making 32 - 17 = 15.
In number series, if differences don't show a clear pattern immediately, calculate the 'difference of differences'тАФit often reveals a simple arithmetic sequence.
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