In the number series 7, 10, 16, 28, 52, 100, the next term is _______. – UGC NET Question

The differences between the terms are 3, 6, 12, 24 and 48. Each difference is double the previous one, forming a geometric pattern at the second level. The next difference should therefore be 96. Adding 96 to the last term 100 gives 100 + 96 = 196. This continuation respects the doubling rule in the differences.

Option A:
Option A gives 184, whose difference from 100 is 84, not the expected 96. This breaks the doubling pattern governing the increments. Hence, 184 is not consistent with the series structure.

Option B:
Option B offers 188, giving a difference of 88 from 100, again not equal to 96 and incompatible with the second-level rule. Therefore, 188 cannot be accepted as correct.

Option C:
Option C suggests 192, corresponding to a difference of 92 from 100, which still fails to match the precise value 96. This makes the pattern irregular. Thus, 192 is not appropriate.

Option D:
Option D yields 196, which is 96 more than 100 and extends the difference sequence 3, 6, 12, 24, 48, 96 in a fully consistent way. This keeps the series logically sound. Therefore, 196 is the correct next term.