Insert the missing number in the series: 165, 195, 255, 285, 345, ?

Concept: When numbers are written as one long series but actually alternate between two independent series, split the sequence into two sub-series - the terms in odd positions and the terms in even positions - each of which typically follows its own constant common difference.

Application:

1. List the terms by position: 1st = 165, 2nd = 195, 3rd = 255, 4th = 285, 5th = 345, 6th = missing.

2. The odd-position terms 165, 255, 345 differ by 90 each (255 - 165 = 90, 345 - 255 = 90).

3. The even-position terms 195, 285 also differ by 90 (285 - 195 = 90).

4. Apply the same common difference to the even-position series: 285 + 90 = 375, so the missing (6th) term is 375.

Cross-check: 375 is 90 more than 285 and is not equal to any of the terms already given (165, 195, 255, 285, 345), consistent with being the next distinct term of the even-position series.