In the number series 6, 13, 27, 55, 111, the next term is _______. – UGC NET Question

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.