In the number series 7, 20, 41, 70, 107, the next term is _______. – UGC NET Question

The first-level differences are 13, 21, 29 and 37. These differences form an arithmetic progression with common difference 8. To keep this structure, the next difference should be 45. Adding 45 to the last term 107 gives 152, so 152 continues both the original sequence and the pattern among the differences.

Option A:
Option A gives 148, which corresponds to a difference of 41 from 107. This would produce differences 13, 21, 29, 37, 41, making the last increment among gaps equal to 4 instead of 8. Thus 148 does not respect the observed second-level behaviour.

Option B:
Option B gives 150, implying a difference of 43 from 107. The final step among differences would be 6, which still fails to match the constant increment of 8. Hence 150 does not align with the pattern.

Option C:
Option C gives 152, which implies a difference of 45 from 107. The sequence of differences becomes 13, 21, 29, 37, 45 and the increments remain 8 throughout. This perfect consistency at the second level makes 152 the correct next term.

Option D:
Option D gives 154, yielding a difference of 47 from 107. That would make the last increment among differences equal to 10, breaking the simple arithmetic progression. Therefore 154 is not a valid continuation.