jee-main 2024 Q81

jee-main · India · session2_06apr_shift2 Sequences and series, recurrence and convergence Direct term computation from recurrence

Let $\alpha , \beta$ be roots of $x ^ { 2 } + \sqrt { 2 } x - 8 = 0$. If $\mathrm { U } _ { \mathrm { n } } = \alpha ^ { \mathrm { n } } + \beta ^ { n }$, then $\frac { \mathrm { U } _ { 10 } + \sqrt { 2 } \mathrm { U } _ { 9 } } { 2 \mathrm { U } _ { 8 } }$ is equal to $\_\_\_\_$

Let $\alpha , \beta$ be roots of $x ^ { 2 } + \sqrt { 2 } x - 8 = 0$. If $\mathrm { U } _ { \mathrm { n } } = \alpha ^ { \mathrm { n } } + \beta ^ { n }$, then $\frac { \mathrm { U } _ { 10 } + \sqrt { 2 } \mathrm { U } _ { 9 } } { 2 \mathrm { U } _ { 8 } }$ is equal to $\_\_\_\_$

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