csat-suneung 2019 Q29

csat-suneung · South-Korea · csat__math-humanities 4 marks Arithmetic Sequences and Series Arithmetic-Geometric Hybrid Problem
An arithmetic sequence $\left\{ a _ { n } \right\}$ with first term a natural number and common difference a negative integer, and a geometric sequence $\left\{ b _ { n } \right\}$ with first term a natural number and common ratio a negative integer, satisfy the following conditions. Find the value of $a _ { 7 } + b _ { 7 }$. [4 points] (가) $\sum _ { n = 1 } ^ { 5 } \left( a _ { n } + b _ { n } \right) = 27$ (나) $\sum _ { n = 1 } ^ { 5 } \left( a _ { n } + \left| b _ { n } \right| \right) = 67$ (다) $\sum _ { n = 1 } ^ { 5 } \left( \left| a _ { n } \right| + \left| b _ { n } \right| \right) = 81$
An arithmetic sequence $\left\{ a _ { n } \right\}$ with first term a natural number and common difference a negative integer, and a geometric sequence $\left\{ b _ { n } \right\}$ with first term a natural number and common ratio a negative integer, satisfy the following conditions. Find the value of $a _ { 7 } + b _ { 7 }$. [4 points]\\
(가) $\sum _ { n = 1 } ^ { 5 } \left( a _ { n } + b _ { n } \right) = 27$\\
(나) $\sum _ { n = 1 } ^ { 5 } \left( a _ { n } + \left| b _ { n } \right| \right) = 67$\\
(다) $\sum _ { n = 1 } ^ { 5 } \left( \left| a _ { n } \right| + \left| b _ { n } \right| \right) = 81$