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考点17 等差数列 1.等差数列的定义: 一般地,如果一个数列从________起,每一项与它的前一项的________都等于____________,那么这个数列就叫作等差数列,这个常数叫作等差数列的________,用字母________表示,即____________(n≥2,且n∈N*). (1)判断(或证明)一个数列是等差数列,可以用式子____________(n∈N*,n>1)或____________(n∈N*). (2)若三个数成等差数列,则可设这三个数分别为________________. 2.等差数列的通项公式: 等差数列{an}的首项为a1,公差是d,则其通项公式为____________________. 3.等差中项: 如果a,A,b成_________,则A叫做a和b的_________,且有A=_________. 4.等差数列的前n项公式:Sn=____________=____________. 5.等差数列的简单性质: (1)等距性:若m+n=p+q,则____________. 特别地,若m+n=2s,则_____________. (2)通项公式的推广:an=am+________d. (3)当d≠0时,an是n的________函数,Sn是n的________函数; 当d=0时,an=________,Sn=________. (4)若等差数列的前n项和为Sn,则Sn,(S2n-Sn),(S3n-S2n),...也成等差数列.
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