In the number series 2, 6, 18, 54, 162, the next term is _______. – UGC NET Question

The series is a geometric progression with common ratio 3. Each term is obtained by multiplying the previous term by 3: 2 × 3 = 6, 6 × 3 = 18, 18 × 3 = 54 and 54 × 3 = 162. To continue this pattern, we multiply 162 by 3 to get 162 × 3 = 486. This maintains the constant ratio throughout the sequence.

Option A:
Option A gives 432, which would correspond to multiplying 162 by a factor less than 3 and does not follow the geometric rule. This breaks the constant ratio pattern. Hence, 432 is not correct.

Option B:
Option B offers 450, which is not 162 multiplied by any simple integer ratio used earlier in the series and appears arbitrary. Therefore, 450 cannot be accepted as consistent with the pattern.

Option C:
Option C suggests 480, which again is not equal to 162 × 3 and would require changing the ratio at the end of the series. This disrupts the geometric progression. Thus, 480 is not appropriate.

Option D:
Option D yields 486, which is exactly 162 × 3 and preserves the common ratio of 3. The expanded sequence 2, 6, 18, 54, 162, 486 is a clean geometric progression. Hence, 486 is the correct next term.