等差數列求和 Lesson Slides: 6 Slides (Grade 10)

6 Slides • 3 Questions

1

等差數列求和

2

Match

等差數列公式配對

通項公式

求和公式1

求和公式2

等差中項

$a_n=a_1+\left(n-1\right)d$

$S_n=\frac{\left(a_1+a_n\right)\times n}{2}$

$S_n=na_1+\frac{n\left(n-1\right)\times d}{2}$

$A=\frac{a+b}{2}$

3

Multiple Choice

計算1＋3＋5＋7＋……＋19的和，則下列哪一個列式是正確的？

1

$\frac{(1＋19)\times19}{2}$

2

$\frac{(1＋19)\times10}{2}$

3

$9\times1+\frac{9\times8}{2}\times2$

4

$19\times1+\frac{19\times18}{2}\times2$

4

Draw

求數列所有項的和:

5

例4. 考慮等差數列-25, -21, -17, …, 求該數列由第21項至第30項之和

6

例. 求1至300間能被6整除之一切整數之和。

7

例. 求1至500間能被6或9整除之一切整數之和。

8

9

已知等差数列的前n项和为𝑺_n，若𝒂₁=𝟏𝟎，公差d=-2，则𝑺_n是否存在最大值？若存在，求𝑺_𝒏的最大值及取得最大值是n的值；若不存在，说明理由.

等差數列求和

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