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# 等差序列导论

## 什么是数列？

• 3, 5, 7 ...
• 21, 16, 11, 6 ...
• 1, 2, 4, 8 ...

$3,$$5,$$7,\text{…}$
$↑$$↑$$↑$

$+2\phantom{\rule{0.167em}{0ex}}↷$$+2\phantom{\rule{0.167em}{0ex}}↷$
$3,$$5,$$7,\text{…}$

$+2\phantom{\rule{0.167em}{0ex}}↷$$+2\phantom{\rule{0.167em}{0ex}}↷$$+2\phantom{\rule{0.167em}{0ex}}↷$$+2\phantom{\rule{0.167em}{0ex}}↷$
$3,$$5,$$7,$$9,$$11,\text{…}$

### 看看你的知识掌握地如何

$+5\phantom{\rule{0.167em}{0ex}}↷$$+5\phantom{\rule{0.167em}{0ex}}↷$$+5\phantom{\rule{0.167em}{0ex}}↷$
$3,$$8,$$13,$
$,\text{…}$

$-3\phantom{\rule{0.167em}{0ex}}↷$$-3\phantom{\rule{0.167em}{0ex}}↷$$-3\phantom{\rule{0.167em}{0ex}}↷$
$20,$$17,$$14,$
$,\text{…}$

$×2\phantom{\rule{0.167em}{0ex}}↷$$×2\phantom{\rule{0.167em}{0ex}}↷$$×2\phantom{\rule{0.167em}{0ex}}↷$
$3,$$6,$$12,$
$,\text{…}$

## 什么是等差数列?

$+2\phantom{\rule{0.167em}{0ex}}↷$$+2\phantom{\rule{0.167em}{0ex}}↷$$+2\phantom{\rule{0.167em}{0ex}}↷$
$3,$$5,$$7,$$9,\text{…}$

$-5\phantom{\rule{0.167em}{0ex}}↷$$-5\phantom{\rule{0.167em}{0ex}}↷$$-5\phantom{\rule{0.167em}{0ex}}↷$
$21,$$16,$$11,$$6,\text{…}$

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

## 公差

$+11\phantom{\rule{0.167em}{0ex}}↷$$+11\phantom{\rule{0.167em}{0ex}}↷$$+11\phantom{\rule{0.167em}{0ex}}↷$
$10,$$21,$$32,$$43,\text{…}$
-2，-5，-8，-11...的公差是负3：
$-3\phantom{\rule{0.167em}{0ex}}↷$$-3\phantom{\rule{0.167em}{0ex}}↷$$-3\phantom{\rule{0.167em}{0ex}}↷$
$-2,$$-5,$$-8,$$-11,\text{…}$

### 看看你的知识掌握地如何

2, 8, 14, 20 ...的公差是多少？

$5,2,-1,-4\text{…}$的公差是多少？

$1,\phantom{\rule{0.167em}{0ex}}1\frac{1}{3},1\frac{2}{3},\phantom{\rule{0.167em}{0ex}}2,\text{…}$的公差是多少？