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If α , β are the roots of the equation x 2 – x – 1 = 0 and S n = 2023 α n + 2024 β n , then:

1. S 11 = S 10 + S 12
2. 2S 11 = S 12 + S 10
3. 2S 12 = S 11 + S 10
4. S 12 = S 11 + S 10

Correct answer: S 12 = S 11 + S 10

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