csat-suneung 2021 Q21

csat-suneung · South-Korea · csat__math-humanities 4 marks Sequences and series, recurrence and convergence Direct term computation from recurrence
A sequence $\left\{ a _ { n } \right\}$ satisfies $0 < a _ { 1 } < 1$ and the following conditions for all natural numbers $n$: (가) $a _ { 2 n } = a _ { 2 } \times a _ { n } + 1$ (나) $a _ { 2 n + 1 } = a _ { 2 } \times a _ { n } - 2$ If $a _ { 7 } = 2$, what is the value of $a _ { 25 }$? [4 points]
(1) 78
(2) 80
(3) 82
(4) 84
(5) 86 
A sequence $\left\{ a _ { n } \right\}$ satisfies $0 < a _ { 1 } < 1$ and the following conditions for all natural numbers $n$:\\
(가) $a _ { 2 n } = a _ { 2 } \times a _ { n } + 1$\\
(나) $a _ { 2 n + 1 } = a _ { 2 } \times a _ { n } - 2$\\
If $a _ { 7 } = 2$, what is the value of $a _ { 25 }$? [4 points]\\
(1) 78\\
(2) 80\\
(3) 82\\
(4) 84\\
(5) 86
Paper Questions
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