In the number series 3, 13, 31, 57, 91, the next term is _______. – UGC NET Question

The differences between consecutive terms are 10, 18, 26 and 34. These differences themselves form an arithmetic progression where each new difference is 8 more than the previous one. Therefore the next difference should be 42. Adding 42 to 91 gives 133 as the next term. This keeps the pattern at both the series and the difference levels consistent.

Option A:
Option A introduces a difference of 42, extending the sequence of gaps to 10, 18, 26, 34, 42. The increments between these differences are 8, 8, 8 and 8, preserving the arithmetic pattern. Hence 133 fits naturally as the next term.

Option B:
Option B would make the next difference 38, giving 10, 18, 26, 34, 38. The final increment from 34 to 38 is only 4, which breaks the consistent step of 8 seen earlier. Therefore 129 is not consistent with the rule.

Option C:
Option C corresponds to a difference of 44 from 91, creating the gaps 10, 18, 26, 34, 44. The increase from 34 to 44 is 10, not 8, so the progression among differences becomes irregular. Hence 135 cannot be the correct continuation.

Option D:
Option D gives a difference of 46, which results in an increment of 12 from the previous difference 34. This diverges even further from the constant +8 pattern and makes 137 an unsuitable next term.