UGC NET Questions (Paper – 1)

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.

Each term after the first is obtained by multiplying the previous term by 2 and then adding 1. We have 6×2+1 = 13, 13×2+1 = 27, 27×2+1 = 55 and 55×2+1 = 111. Applying the same rule again gives 111×2+1 = 223. Thus 223 is the only option that maintains the consistent recursive transformation.

Option A:
Option A gives 221, which would require subtracting 1 after doubling, i.e., 111×2−1, and introduces a new operation not used earlier. This contradicts the strictly “×2+1” structure observed in the series. Therefore 221 is not the correct continuation.

Option B:
Option B gives 225, which can be written as 111×2+3. This breaks the constant “+1” adjustment and suggests a different, unsupported rule. Hence 225 is not aligned with the series pattern.

Option C:
Option C gives 227, corresponding to 111×2+5, again using a different constant at the end of the multiplication. This has no basis in the previously observed behaviour, so 227 cannot be accepted.

Option D:
Option D gives 223, exactly equal to 111×2+1. It extends the same recursive rule that generates every earlier term, keeping the pattern simple and coherent. For this reason, 223 is the correct next term.