taiwan-gsat 2020 Q5

taiwan-gsat · Other · ast__math-b 8 marks Geometric Sequences and Series True/False or Multiple-Statement Verification

A sequence $a _ { 1 } , a _ { 2 } , \cdots$ where the odd-indexed terms form a geometric sequence with common ratio $\frac { 1 } { 3 }$ , and the even-indexed terms form a geometric sequence with common ratio $\frac { 1 } { 2 }$ , with $a _ { 1 } = 3 , a _ { 2 } = 2$ . Select the correct options.
(1) $a _ { 4 } > a _ { 5 } > a _ { 6 } > a _ { 7 }$
(2) $\frac { a _ { 10 } } { a _ { 11 } } > 10$
(3) $\lim _ { n \rightarrow \infty } a _ { n } = 0$
(4) $\lim _ { n \rightarrow \infty } \frac { a _ { n + 1 } } { a _ { n } } = 0$
(5) $\sum _ { n = 1 } ^ { 100 } a _ { n } > 9$

A sequence $a _ { 1 } , a _ { 2 } , \cdots$ where the odd-indexed terms form a geometric sequence with common ratio $\frac { 1 } { 3 }$ , and the even-indexed terms form a geometric sequence with common ratio $\frac { 1 } { 2 }$ , with $a _ { 1 } = 3 , a _ { 2 } = 2$ . Select the correct options.\\
(1) $a _ { 4 } > a _ { 5 } > a _ { 6 } > a _ { 7 }$\\
(2) $\frac { a _ { 10 } } { a _ { 11 } } > 10$\\
(3) $\lim _ { n \rightarrow \infty } a _ { n } = 0$\\
(4) $\lim _ { n \rightarrow \infty } \frac { a _ { n + 1 } } { a _ { n } } = 0$\\
(5) $\sum _ { n = 1 } ^ { 100 } a _ { n } > 9$

Paper Questions

QA QB QC QD QI QII Q1 Q2 Q3 Q4 Q5 Q6