Find the next term from alternating +30 and +60 jumps: 165, 195, 255, 285, 345, ( ? )

Introduction / Context:
This is a difference-pattern series using a repeating two-step increment. Identifying the increment cycle enables direct computation of the next term.

Given Data / Assumptions:

• Sequence: 165, 195, 255, 285, 345, ( ? )
• Differences observed: +30, +60, +30, +60, …

Concept / Approach:
Apply the same two-step cycle to extend the series: after +60 from 285 to 345, the next jump should revert to +30.

Step-by-Step Solution:
165 + 30 = 195195 + 60 = 255255 + 30 = 285285 + 60 = 345345 + 30 = 375

Verification / Alternative check:
The strict repetition (+30, +60) leaves no ambiguity; 375 uniquely fits.

Why Other Options Are Wrong:
420 and 435 would require +75 or +90; 390 implies +45; 360 is − or +15 shift; none match the cycle.

Common Pitfalls:
Assuming a single arithmetic progression; the alternating increments are essential.

Final Answer:
375