csat-suneung 2022 Q5

csat-suneung · South-Korea · csat__math 3 marks Sequences and series, recurrence and convergence Summation of sequence terms

For a sequence $\left\{ a _ { n } \right\}$ with first term 1, satisfying for all natural numbers $n$: $$a _ { n + 1 } = \begin{cases} 2 a _ { n } & \left( a _ { n } < 7 \right) \\ a _ { n } - 7 & \left( a _ { n } \geq 7 \right) \end{cases}$$ what is the value of $\sum _ { k = 1 } ^ { 8 } a _ { k }$? [3 points]
(1) 30
(2) 32
(3) 34
(4) 36
(5) 38

For a sequence $\left\{ a _ { n } \right\}$ with first term 1, satisfying for all natural numbers $n$:
$$a _ { n + 1 } = \begin{cases} 2 a _ { n } & \left( a _ { n } < 7 \right) \\ a _ { n } - 7 & \left( a _ { n } \geq 7 \right) \end{cases}$$
what is the value of $\sum _ { k = 1 } ^ { 8 } a _ { k }$? [3 points]\\
(1) 30\\
(2) 32\\
(3) 34\\
(4) 36\\
(5) 38

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