csat-suneung 2020 Q21

csat-suneung · South-Korea · csat__math-humanities 4 marks Sequences and series, recurrence and convergence Summation of sequence terms
The sequence $\left\{ a _ { n } \right\}$ satisfies the following conditions for all natural numbers $n$. (가) $a _ { 2 n } = a _ { n } - 1$ (나) $a _ { 2 n + 1 } = 2 a _ { n } + 1$ When $a _ { 20 } = 1$, what is the value of $\sum _ { n = 1 } ^ { 63 } a _ { n }$? [4 points]
(1) 704
(2) 712
(3) 720
(4) 728
(5) 736 
The sequence $\left\{ a _ { n } \right\}$ satisfies the following conditions for all natural numbers $n$.\\
(가) $a _ { 2 n } = a _ { n } - 1$\\
(나) $a _ { 2 n + 1 } = 2 a _ { n } + 1$\\
When $a _ { 20 } = 1$, what is the value of $\sum _ { n = 1 } ^ { 63 } a _ { n }$? [4 points]\\
(1) 704\\
(2) 712\\
(3) 720\\
(4) 728\\
(5) 736
Paper Questions
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