Pattern of escalating exponents on D, E, F: complete DEF, DEF2, DE2F2, ____, D2E2F3 by identifying the leftward sweep of exponent increments to fill in the missing fourth term.

Difficulty: Medium

Correct Answer: D2E2F2

Explanation:

View each string as D^a E^b F^c, where omitted exponents equal 1. Exponents increase by +1 one letter at a time, cycling right-to-left.

  • Term 1: D1E1F1 (shown as DEF).
  • Term 2: D1E1F2 (increment F).
  • Term 3: D1E2F2 (increment E).
  • Term 4: D2E2F2 (increment D) ⇒ missing term.
  • Term 5: D2E2F3 (increment F again) — given.

Concept/Approach
Recognize the incremental sweep of exponents: F ↑, then E ↑, then D ↑, then F ↑ again, …
Step-by-Step calculation
1) After DE2F2, increment D's exponent: 1 → 2.2) Keep E and F at 2: compose D2E2F2.
Verification/Alternative
The provided last term D2E2F3 confirms the cycle restarting at F.
Common pitfalls
Jumping multiple exponents in one term or changing letter order.
Final Answer
D2E2F2

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