In the number series 1, 5, 17, 53, the next term is _______. – UGC NET Question

Each term after the first equals three times the previous term plus 2. We see 1×3+2 = 5, 5×3+2 = 17 and 17×3+2 = 53. Applying this rule again gives 53×3+2 = 159+2 = 161. Therefore, 161 is the correct next term in the sequence.

Option A:
Option A is 150, which would correspond to 53×3−9 and does not follow the "+2" pattern. No earlier step subtracts anything, so this is inconsistent. Hence, 150 cannot be correct.

Option B:
Option B is 155, implying 53×3−4 or some other ad hoc adjustment. This does not match the fixed addition of 2 visible in all previous transitions. Therefore, 155 is not suitable.

Option C:
Option C is 157, which does not arise from 53×3 plus a constant consistent with earlier terms. Using 157 would produce an irregular change. Thus, it breaks the simple rule.

Option D:
Option D equals 161 and is exactly 53×3+2, preserving the recursive relationship. The series 1, 5, 17, 53, 161 clearly shows the same operation being applied repeatedly. This makes 161 the correct answer.