Solve this multiple-choice question and choose the correct option.

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:.

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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

D2E2F2
D2EF2
DE2F3
D3E2F2
D2E3F2

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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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.

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