csat-suneung 2022 Q18

csat-suneung · South-Korea · csat__math 3 marks Sequences and Series Evaluation of a Finite or Infinite Sum

For a sequence $\left\{ a _ { n } \right\}$, $$\sum _ { k = 1 } ^ { 10 } a _ { k } - \sum _ { k = 1 } ^ { 7 } \frac { a _ { k } } { 2 } = 56 , \quad \sum _ { k = 1 } ^ { 10 } 2 a _ { k } - \sum _ { k = 1 } ^ { 8 } a _ { k } = 100$$ find the value of $a _ { 8 }$. [3 points]

For a sequence $\left\{ a _ { n } \right\}$,
$$\sum _ { k = 1 } ^ { 10 } a _ { k } - \sum _ { k = 1 } ^ { 7 } \frac { a _ { k } } { 2 } = 56 , \quad \sum _ { k = 1 } ^ { 10 } 2 a _ { k } - \sum _ { k = 1 } ^ { 8 } a _ { k } = 100$$
find the value of $a _ { 8 }$. [3 points]

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