In the number series 2, 6, 18, 54, the next term is _______. – UGC NET Question

Each term is three times the previous one: 2×3 = 6, 6×3 = 18 and 18×3 = 54. This defines a geometric progression with common ratio 3. Multiplying the last term 54 by 3 gives 162. Thus, 162 is the next term that keeps the series consistent.

Option A:
Option A suggests 72, which is only 18 more than 54 and does not fit the multiplication-by-three rule. None of the earlier transitions involve adding a fixed number like 18. Therefore, 72 is not appropriate.

Option B:
Option B is 90, which represents 54 plus 36 and again breaks the pure multiplication pattern. The series has never used addition rules, so introducing such a change would be unjustified. Hence, 90 is incorrect.

Option C:
Option C equals 162 and results directly from 54×3, preserving the ratio of 3 between consecutive terms. The extended series 2, 6, 18, 54, 162 shows a clear and consistent geometric pattern. This makes 162 the valid next term.

Option D:
Option D is 180, which does not arise from multiplying 54 by a whole number used earlier in the sequence. Choosing 180 would produce a ratio of 10/3 with the previous term, not 3. Thus, this option does not respect the established rule.