Sequence and Series: JEE Main 2025 Mathematics question

Let $\langle a_n \rangle$ be a sequence such that $a_0 = 0$, $a_1 = \frac{1}{2}$ and $2 a_{n+2} = 5 a_{n+1} - 3 a_n$, $n = 0, 1, 2, 3, \ldots$. Then $\sum_{k=1}^{100} a_k$ is equal to