In the number series 4, 7, 13, 25, 49, 97, 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 progression at the second level. The next difference should therefore be 96. Adding 96 to the last term 97 gives 97 + 96 = 193, which follows this doubling pattern exactly.

Option A:
Option A gives 187, corresponding to a difference of 90 from 97, which does not match the required next difference of 96. This breaks the doubling rule that defines the series. Hence, 187 is not consistent with the pattern.

Option B:
Option B offers 189, giving a difference of 92 from 97 and again failing to match the expected 96. This disrupts the geometric progression in the differences. Therefore, 189 cannot be accepted.

Option C:
Option C suggests 191, whose difference from 97 is 94, still not the correct doubled value of 48. This makes the second-level pattern inconsistent. Thus, 191 is not appropriate.

Option D:
Option D yields 193, which is 96 more than 97 and continues the difference sequence 3, 6, 12, 24, 48, 96 in a perfectly structured way. This maintains the integrity of the series. Hence, 193 is the correct next term.