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# 等差序列公式导论

## 公式是什么?

3, comma, 5, comma, 7, comma, point, point, point

na, left parenthesis, n, right parenthesis
(序数)(序数n对应的数值)
13
25
37

### 看看你的知识掌握地如何

1) 找到3, 5, 7, ...中的a, left parenthesis, 4, right parenthesis
a, left parenthesis, 4, right parenthesis, equals

2)对于任何序数na, left parenthesis, n, minus, 1, right parenthesis 是多少？

## 递推公式和等差数列

1. 一个数列的第一个序数
2. 通过序列中前一个数去得到后一个数的规律模式

$\begin{cases}a(1) = 3&\leftarrow\gray{\text{第一个数是3}}\\\\ a(n) = a(n-1)+2&\leftarrow\gray{\text{在前面数的基础上加上2}} \end{cases}$

a, left parenthesis, n, right parenthesisequals, a, left parenthesis, n, minus, 1, right parenthesis, plus, 2
a, left parenthesis, 1, right parenthesisequals, start color #11accd, 3, end color #11accd
a, left parenthesis, 2, right parenthesisequals, a, left parenthesis, 1, right parenthesis, plus, 2equals, start color #11accd, 3, end color #11accd, plus, 2equals, start color #aa87ff, 5, end color #aa87ff
a, left parenthesis, 3, right parenthesisequals, a, left parenthesis, 2, right parenthesis, plus, 2equals, start color #aa87ff, 5, end color #aa87ff, plus, 2equals, start color #1fab54, 7, end color #1fab54
a, left parenthesis, 4, right parenthesisequals, a, left parenthesis, 3, right parenthesis, plus, 2equals, start color #1fab54, 7, end color #1fab54, plus, 2equals, start color #e07d10, 9, end color #e07d10
a, left parenthesis, 5, right parenthesisequals, a, left parenthesis, 4, right parenthesis, plus, 2equals, start color #e07d10, 9, end color #e07d10, plus, 2equals, 11


### 看看你的知识掌握地如何

3) 通过这个公式找到b, left parenthesis, 4, right parenthesis的值 $\begin{cases}b(1)=-5\\\\ b(n)=b(n-1)+9 \end{cases}$
b, left parenthesis, 4, right parenthesis, equals

4) 通过这个公式找到 c, left parenthesis, 3, right parenthesis 的值$\begin{cases}c(1)=20\\\\ c(n)=c(n-1)-17 \end{cases}$
c, left parenthesis, 3, right parenthesis, equals

5) 通过这个公式找到 d, left parenthesis, 5, right parenthesis 的值 $\begin{cases}d(1)=2\\\\ d(n)=d(n-1)+0.4 \end{cases}$
d, left parenthesis, 5, right parenthesis, equals

## 等差数列的通项公式

a, left parenthesis, n, right parenthesis, equals, 3, plus, 2, left parenthesis, n, minus, 1, right parenthesis

\begin{aligned}a(\greenE 5)&=3+2(\greenE 5-1)\\\\ &=3+2\cdot4\\\\ &=3+8\\\\ &=11\end{aligned}

### 看看你的知识掌握地如何

6) 通过 b, left parenthesis, n, right parenthesis, equals, minus, 5, plus, 9, left parenthesis, n, minus, 1, right parenthesis 找到序列中 b, left parenthesis, 10, right parenthesis 的值
b, left parenthesis, 10, right parenthesis, equals

7) 通过 c, left parenthesis, n, right parenthesis, equals, 20, minus, 17, left parenthesis, n, minus, 1, right parenthesis 找到序列中 c, left parenthesis, 8, right parenthesis 的值
c, left parenthesis, 8, right parenthesis, equals

8) 通过 d, left parenthesis, n, right parenthesis, equals, 2, plus, 0, point, 4, left parenthesis, n, minus, 1, right parenthesis 找到序列中 d, left parenthesis, 21, right parenthesis 的值
d, left parenthesis, 21, right parenthesis, equals

## 序列就是函数

### 反思题

9) 用那种公式来找到一个序列的第100个数会更快？

### 挑战问题

10) 一个等差数列的显示公式是 f, left parenthesis, n, right parenthesis, equals, 3, minus, 4, left parenthesis, n, minus, 1, right parenthesis.

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