gaokao 2022 Q17

gaokao · China · national-A-science 12 marks Arithmetic Sequences and Series Multi-Part Structured Problem on AP

Let $S _ { n }$ denote the sum of the first $n$ terms of the sequence $\left\{ a _ { n } \right\}$. Given that $\frac { 2 S _ { n } } { n } + n = 2 a _ { n } + 1$.
(1) Prove that $\left\{ a _ { n } \right\}$ is an arithmetic sequence;
(2) If $a _ { 4 }$, $a _ { 7 }$, $a _ { 9 }$ form a geometric sequence, find the minimum value of $S _ { n }$.

Let $S _ { n }$ denote the sum of the first $n$ terms of the sequence $\left\{ a _ { n } \right\}$. Given that $\frac { 2 S _ { n } } { n } + n = 2 a _ { n } + 1$.\\
(1) Prove that $\left\{ a _ { n } \right\}$ is an arithmetic sequence;\\
(2) If $a _ { 4 }$, $a _ { 7 }$, $a _ { 9 }$ form a geometric sequence, find the minimum value of $S _ { n }$.

Paper Questions

Q1 Q4 Q5 Q6 Q9 Q10 Q13 Q14 Q15 Q16 Q17 Q18 Q19 Q21 Q22 Q23