jee-main 2024 Q61

jee-main · India · session2_06apr_shift1 Sequences and series, recurrence and convergence Multiple-choice on sequence properties

Let $\alpha , \beta$ be the distinct roots of the equation $x ^ { 2 } - \left( t ^ { 2 } - 5 t + 6 \right) x + 1 = 0 , t \in \mathbb { R }$ and $a _ { n } = \alpha ^ { n } + \beta ^ { n }$. Then the minimum value of $\frac { a _ { 2023 } + a _ { 2025 } } { a _ { 2024 } }$ is
(1) $- 1 / 4$
(2) $- 1 / 4$
(3) $- 1 / 2$
(4) $1 / 4$

Let $\alpha , \beta$ be the distinct roots of the equation $x ^ { 2 } - \left( t ^ { 2 } - 5 t + 6 \right) x + 1 = 0 , t \in \mathbb { R }$ and $a _ { n } = \alpha ^ { n } + \beta ^ { n }$. Then the minimum value of $\frac { a _ { 2023 } + a _ { 2025 } } { a _ { 2024 } }$ is\\
(1) $- 1 / 4$\\
(2) $- 1 / 4$\\
(3) $- 1 / 2$\\
(4) $1 / 4$

Paper Questions

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