The given series multiplies each term by a constant factor to obtain the next one. Specifically, 9 ÷ 3 = 3, 27 ÷ 9 = 3 and 81 ÷ 27 = 3, so the common ratio is 3. To continue the pattern, we multiply 81 by 3 to obtain the next term. This gives 81 × 3 = 243, which preserves the geometric progression.
Option A:
Option A, 162, arises if someone incorrectly multiplies by 2 instead of 3, giving 81 × 2. However, this contradicts the established common ratio of 3 used in all previous steps.
Option B:
Option B, 200, does not correspond to any simple multiple of 81 consistent with the progression and seems unrelated to the pattern.
Option C:
Option C, 225, is 15² and may be chosen due to familiarity with square numbers, but it does not follow from multiplying 81 by the common ratio 3.
Option D:
Option D maintains the constant ratio of 3 between consecutive terms. By applying 81 × 3, we get 243, which is the only option that respects the geometric structure of the series.
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