csat-suneung 2022 Q21

csat-suneung · South-Korea · csat__math 4 marks Geometric Sequences and Series Finite Geometric Sum and Term Relationships

A sequence $\left\{ a _ { n } \right\}$ satisfies the following conditions.
(a) $\left| a _ { 1 } \right| = 2$
(b) For all natural numbers $n$, $\left| a _ { n + 1 } \right| = 2 \left| a _ { n } \right|$.
(c) $\sum _ { n = 1 } ^ { 10 } a _ { n } = - 14$ Find the value of $a _ { 1 } + a _ { 3 } + a _ { 5 } + a _ { 7 } + a _ { 9 }$. [4 points]

A sequence $\left\{ a _ { n } \right\}$ satisfies the following conditions.\\
(a) $\left| a _ { 1 } \right| = 2$\\
(b) For all natural numbers $n$, $\left| a _ { n + 1 } \right| = 2 \left| a _ { n } \right|$.\\
(c) $\sum _ { n = 1 } ^ { 10 } a _ { n } = - 14$\\
Find the value of $a _ { 1 } + a _ { 3 } + a _ { 5 } + a _ { 7 } + a _ { 9 }$. [4 points]

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