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### 高中数学多媒体课堂

an

·

·

·

·

·

n

a+b

Ａ＝———

2

1.等差数列的概念

an=a1+(n-1)d

2.等差数列的通项公式

∵ak=a1+(k-1)d, 即a1=ak－(k-1)d.

∴通项公式又可改写为

an=ak+(n-k)d .

3.等差中项

3+15=18,

4+14=18,

5+13=18,

…… ,

6+12=18,

15+3=18,

∴3+4+…+15=

18×13／2=117(根).

n个

2Sn=(a1+an)+(a1+an)+ … +(a1+an)

=n(a1+an)

∴等差数列的前n项和公式是

∵an=a1+(n－1)d,∴公式又可写成

1+2+…+100=(1+100)+(2+99)+…+(55+51)

=101×50=5050.

n(n+1)

2

②在正整数列中，前n个偶数的和是多少？

1＋2＋…＋n=

2 + 4 +…+ 2n=

n(n+1)

∵a1=－10, d=－6－(－10)=4 ,

1.根据条件，求相应等差数列{an}的Sn:

①a1=5, an=95, n=10;

②a1=100, d=－2, n=50;

③a1=14.5, d=0.7, an=32.

②2550；

③604.5

2.等差数列5,4,3,2,…前多少项的和是－30？

(关于n的二次函数)

（机动内容）

7, 14, 21, … , 91, 98.

=735