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Select the number from among the given options that can replace the question mark (?) in the following series. 549 525 477 405 309?
145
167
189
139
189
Calculate the difference between consecutive terms. The differences form a decreasing AP or a pattern of decreasing multiples of cubes/squares or double differences.
Calculate the difference between consecutive terms. The differences form a decreasing AP or a pattern of decreasing multiples of cubes/squares or double differences.
Step 1: Analyze the first two numbers
Find the difference between 549 and 525. 549 - 525 = 24. The series is decreasing.
Step 2: Check subsequent differences
525 - 477 = 48, 477 - 405 = 72, 405 - 309 = 96. The differences are multiples of 24 (-24, -48, -72, -96).
Step 3: Calculate the missing term
The next difference must be -120 (24 x 5). Subtracting 120 from 309 gives 309 - 120 = 189.
A: 145 is incorrect because subtracting -120 from 309 yields 189, not 145. B: 167 is incorrect as it does not follow the multiple of 24 subtraction pattern. D: 139 is incorrect and results from faulty arithmetic.
C is correct because the series follows a decreasing pattern with consecutive differences of multiples of 24 (-24, -48, -72, -96, -120), giving 309 - 120 = 189.
When numbers in a series decrease at an increasing rate, always compute the first and second differences to easily spot arithmetic progressions or multiplication tables hidden in the differences.
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