The differences between successive terms are 3, 9, 27 and 81. Each difference is obtained by multiplying the previous difference by 3, forming a geometric progression at the second level. The next difference should therefore be 81 × 3 = 243. Adding 243 to the last term 122 gives 122 + 243 = 365, which continues the pattern exactly.
Option A:
Option A gives 362, corresponding to a difference of 240 from 122, which does not match the expected value of 243. This breaks the geometric pattern in the differences. Therefore, 362 is not consistent with the rule.
Option B:
Option B offers 364, yielding a difference of 242 from 122, one less than the required 243, and again failing to preserve the exact growth in differences. Hence, 364 cannot be accepted as correct.
Option C:
Option C yields 365, which is 243 more than 122 and matches the predicted next difference in the geometric sequence 3, 9, 27, 81, 243. This keeps both the main series and the second-level pattern in harmony. Thus, 365 is the correct next term.
Option D:
Option D suggests 368, giving a difference of 246 from 122, which overshoots the expected difference and disrupts the clean factor-of-three rule. Therefore, 368 is not a valid continuation.
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