csat-suneung 2018 Q13

csat-suneung · South-Korea · csat__math-humanities 3 marks Sequences and series, recurrence and convergence Direct term computation from recurrence
The sequence $\left\{ a _ { n } \right\}$ has $a _ { 1 } = 2$, and for all natural numbers $n$, $$a _ { n + 1 } = \begin{cases} a _ { n } - 1 & \text{(when } a _ { n } \text{ is even)} \\ a _ { n } + n & \text{(when } a _ { n } \text{ is odd)} \end{cases}$$ Find the value of $a _ { 7 }$. [3 points]
(1) 7
(2) 9
(3) 11
(4) 13
(5) 15 
The sequence $\left\{ a _ { n } \right\}$ has $a _ { 1 } = 2$, and for all natural numbers $n$,
$$a _ { n + 1 } = \begin{cases} a _ { n } - 1 & \text{(when } a _ { n } \text{ is even)} \\ a _ { n } + n & \text{(when } a _ { n } \text{ is odd)} \end{cases}$$
Find the value of $a _ { 7 }$. [3 points]\\
(1) 7\\
(2) 9\\
(3) 11\\
(4) 13\\
(5) 15
Paper Questions
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