Let ⟨ aₙ ⟩ be a sequence such that a₀ = 0, a₁ = 1/2, and 2aₙ₊₂ =… | JEE Main 2025 Mathematics PYQ

MCQMediumJEE Main 2025 · 28 January, Shift 1Sum of Series

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

A
$3a_{99} + 100$
B
$3a_{99} - 100$
C
$3a_{100} + 100$
D
$3a_{100} - 100$

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