csat-suneung 2019 Q13

csat-suneung · South-Korea · csat__math-humanities 3 marks Sequences and Series Recurrence Relations and Sequence Properties
A sequence $\left\{ a _ { n } \right\}$ has $a _ { 1 } = 2$ and satisfies for all natural numbers $n$: $$a _ { n + 1 } = \left\{ \begin{array} { c c } \frac { a _ { n } } { 2 - 3 a _ { n } } & ( \text{when } n \text{ is odd} ) \\ 1 + a _ { n } & ( \text{when } n \text{ is even} ) \end{array} \right.$$ What is the value of $\sum _ { n = 1 } ^ { 40 } a _ { n }$? [3 points]
(1) 30
(2) 35
(3) 40
(4) 45
(5) 50
A sequence $\left\{ a _ { n } \right\}$ has $a _ { 1 } = 2$ and satisfies for all natural numbers $n$:
$$a _ { n + 1 } = \left\{ \begin{array} { c c } 
\frac { a _ { n } } { 2 - 3 a _ { n } } & ( \text{when } n \text{ is odd} ) \\
1 + a _ { n } & ( \text{when } n \text{ is even} )
\end{array} \right.$$
What is the value of $\sum _ { n = 1 } ^ { 40 } a _ { n }$? [3 points]\\
(1) 30\\
(2) 35\\
(3) 40\\
(4) 45\\
(5) 50