Question:

Fill in the blank: 
257, 291, ______, 365, 405

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When two consecutive gaps are visible, test if differences themselves form an arithmetic progression.
Updated On: Aug 14, 2025
  • 313
  • 322
  • 327
  • 343
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The Correct Option is C

Solution and Explanation

We need to identify the missing number in the sequence: 257, 291, ______, 365, 405.

The best approach is to first determine the pattern or rule governing the sequence. Let's calculate the difference between consecutive terms where possible:

  • From 257 to 291: 291 - 257 = 34
  • From 365 to 405: 405 - 365 = 40

We hypothesize that the differences might increment by a constant value. The difference might form an arithmetic sequence. To test this, we calculate the difference increase from 34 to 40:

  • Increase from 34 to 40: 40 - 34 = 6

Therefore, we suspect the missing difference between 291 and the missing middle number could be 34 + 6 = 40.

Using this logic:

  • From 291 to the missing number: 291 + 36 = 327

Thus, the missing number that fits the sequence is 327, as the differences would become 34, 36, 38, and 40, showing a steady increment of 2 in the difference values.

Therefore, the correct answer is: 327

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