In the number series 1, 3, 7, 15, 31, the next term is _______. – UGC NET Question

The differences between consecutive terms are 2, 4, 8 and 16. These are powers of two doubling at each step. To continue this pattern, the next difference should be 32. Adding 32 to the last term 31 gives 31 + 32 = 63, which extends the series in a perfectly consistent way.

Option A:
Option A gives 61, which corresponds to a difference of 30 from 31 and fails to match the next power of two. Since the previous differences are 2, 4, 8 and 16, the logical continuation is 32, not 30. Hence, 61 is not correct.

Option B:
Option B yields 63, which is 32 more than 31 and completes the power-of-two difference sequence 2, 4, 8, 16, 32. The pattern remains clean and conceptually strong. Therefore, 63 is the correct next term.

Option C:
Option C suggests 65, giving a difference of 34 from 31, which does not fit into the powers-of-two framework. Such an increment is arbitrary with respect to the earlier differences. Thus, 65 cannot be accepted.

Option D:
Option D offers 67, which is 36 greater than 31 and again unrelated to the powers-of-two idea. Using 67 would disrupt the elegant second-level pattern that defines the series. Therefore, 67 is not the right answer.