In the number series 5, 8, 16, 19, 38, 41, 82, the next term is _______. – UGC NET Question

This series alternates between adding 3 and multiplying by 2. Starting with 5, we have 5 + 3 = 8, 8 × 2 = 16, 16 + 3 = 19, 19 × 2 = 38, 38 + 3 = 41 and 41 × 2 = 82. The next operation should be addition by 3. Thus, the next term is 82 + 3 = 85, which continues the alternating pattern exactly.

Option A:
Option A gives 83, which would require adding only 1 to 82 and introduces a new increment not used previously. This breaks the uniform "+3, then ×2" rule. Therefore, 83 is not consistent with the pattern.

Option B:
Option B offers 84, whose difference from 82 is 2, again incompatible with the fixed addition of 3 in the pattern. This makes the series irregular. Hence, 84 cannot be accepted.

Option C:
Option C suggests 87, which requires adding 5 to 82 and does not conform to the standard "+3" step seen throughout. This disrupts the structured alternation. Thus, 87 is not appropriate.

Option D:
Option D yields 85, which is exactly 82 + 3 and matches the next stage of the "+3, then ×2" cycle. The series 5, 8, 16, 19, 38, 41, 82, 85 remains coherent. Therefore, 85 is the correct next term.