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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? 361, 348, 335, 322, 309,?
290
300
296
294
296
Observe that the numbers are decreasing at a constant rate. Find the common difference by subtracting consecutive terms (361 - 348 = 13), and subtract this same difference from the last given term.
Observe that the numbers are decreasing at a constant rate. Find the common difference by subtracting consecutive terms (361 - 348 = 13), and subtract this same difference from the last given term.
Step 1: Calculate the difference between consecutive terms
361 - 348 = 13, 348 - 335 = 13, 335 - 322 = 13, and 322 - 309 = 13.
Step 2: Identify the pattern rule
The series is an arithmetic progression with a common difference of -13 (subtracting 13 at each step).
Step 3: Apply the rule to find the missing term
Subtract 13 from the last given term: 309 - 13 = 296.
A: 290 is incorrect because 309 - 19 equals 290, which does not match the -13 common difference. B: 300 is incorrect because it implies a difference of -9, which violates the established -13 rule. D: 294 is incorrect because 309 - 15 equals 294, not matching the -13 pattern.
C is correct because the series follows a consistent arithmetic subtraction pattern of minus 13 at each step, giving 309 minus 13 equals 296.
Always test both arithmetic (subtraction/addition) and geometric (multiplication/division) differences when first approaching any numerical series in competitive exams.
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