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Which of the following options should come in place of the question mark (?) in the given series to make it logically complete? 33, 41, 57, 89, 153,?
269
297
253
281
281
Look for differences between consecutive numbers: the differences themselves follow a pattern of powers of 2 (8, 16, 32, 64, 128).
Look for differences between consecutive numbers: the differences themselves follow a pattern of powers of 2 (8, 16, 32, 64, 128).
Analyze Differences
Calculate the difference between consecutive numbers: 41-33 = 8; 57-41 = 16; 89-57 = 32; 153-89 = 64.
Identify Pattern
The differences are powers of 2 (or doubling each time): 8, 16, 32, 64. The next difference must be 64 x 2 = 128.
Calculate Final Term
Add the next difference to the last known term: 153 + 128 = 281.
A: 269 is incorrect; B: 297 is incorrect; C: 253 is incorrect. The calculation consistently yields 281.
D is correct because the series follows an addition pattern where the increment doubles at each step (8, 16, 32, 64, 128), leading to 153 + 128 = 281.
If the differences in a series grow rapidly, always check for multiplication, powers of 2, or squares/cubes first.
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