Try Finding The First Few Terms!

\[ \large a_{i}= 2a_{i-1} −a_{i-2} +2 \]

Define the sequence \({(a_{n}})\) with intial terms \(a_{0} = 0, a_{1} = 1\), satisfying the recurrence relations above for all \( i \geq 2.\) Determine the value of \(a_{1000}\).

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