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Select the number from among the given options that can replace the question mark (?) in the following series. 175221267313359?
413
431
405
429
405
Observe the constant difference between consecutive terms. Since the difference is uniform, simply add that common difference to the last term.
Observe the constant difference between consecutive terms. Since the difference is uniform, simply add that common difference to the last term.
Step 1: Calculate Difference between 1st and 2nd term
221 - 175 = 46
Step 2: Calculate Difference between subsequent terms
267 - 221 = 46, 313 - 267 = 46, and 359 - 313 = 46. The common difference is consistently +46.
Step 3: Find the missing term
Add 46 to the last given term: 359 + 46 = 405.
A: 413 is incorrect because adding 46 to 359 gives 405, not 413. B: 431 is incorrect and does not follow the +46 arithmetic sequence. D: 429 is incorrect as it deviates from the constant +46 step.
C is correct because the series follows a constant arithmetic progression with a common difference of +46, and 359 + 46 = 405.
Always check the difference between consecutive terms first when dealing with numerical series. If differences are constant, it is a simple arithmetic progression.
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