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# 几何序列复习

## 等比数列的构成与公式

$×2\phantom{\rule{0.167em}{0ex}}↷$$×2\phantom{\rule{0.167em}{0ex}}↷$$×2\phantom{\rule{0.167em}{0ex}}↷$
$1,$$2,$$4,$$8,\text{…}$

$a\left(n\right)=k\cdot {r}^{n-1}$

$\left\{\begin{array}{l}a\left(1\right)=k\\ \\ a\left(n\right)=a\left(n-1\right)\cdot r\end{array}$

## 扩展等比数列

$×\frac{1}{3}\phantom{\rule{0.167em}{0ex}}↷$$×\frac{1}{3}\phantom{\rule{0.167em}{0ex}}↷$
$54,$$18,$$6,\text{…}$

$×\frac{1}{3}\phantom{\rule{0.167em}{0ex}}↷$$×\frac{1}{3}\phantom{\rule{0.167em}{0ex}}↷$$×\frac{1}{3}\phantom{\rule{0.167em}{0ex}}↷$
$54,$$18,$$6,$$2,\text{…}$

## 写出等比数列的递推公式

$\left\{\begin{array}{l}a\left(1\right)=54\\ \\ a\left(n\right)=a\left(n-1\right)\cdot \frac{1}{3}\end{array}$

$\left\{\begin{array}{l}a\left(1\right)=k\\ \\ a\left(n\right)=a\left(n-1\right)\cdot r\end{array}$
$k=$
$r=$

## 写出等比数列的通项公式

$a\left(n\right)=54\cdot {\left(\frac{1}{3}\right)}^{n-1}$

$a\left(n\right)=$