Summation of seriesMedium

Sum of Linear Recurrence Sequence

Let <a_n> be a sequence such that a₀ = 0, a₁ = $\frac{1}{2}$ and 2a_n+2= 5a_n+1 – 3a_n , n = 0, 1, 2, 3, …… Then $\sum\limits_{k = 1}^{100} {{a_k}}$ is equal to :

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