专题巩固提升等差,等比数列的判定判定一个数列是等差或等比数列的常用方法(1)定义法an+1-an=d(常数){an}是等差数列.=q(非零常数){an}是等比数列.(2)中项公式法2an+1=an+an+2(n∈N*){an}是等差数列.=anan+2(anan+1an+2≠0){an}为等比数列.n1naa2n1a(3)通项公式法an=pn+q(p,q为常数){an}是等差数列.an=c·qn(c,q均为非零常数){an}是等比数列.(4)前n项和公式Sn=An2+Bn(A、B均为常数){an}是等差数列.Sn=kqn-k(k为常数,且q≠0,1){an}是等比数列.1.定义法{}1.{}=3+2{}anan已知数列是等差数列,在数列b中,nb,求证数列b是等例差数列.nn1n{}{.a1}naan+1n已知数列满足=1,a=2a+1,变式训求证数列是等练比数列.2.中项公式法()log()log0,,2.,mmxcayabzabcm已知(b-c)log若依次成等差,且公差不为零,求证:x,y,z成例等比数列.221,,,11,bcbcacab2已知a成等差数列,求证:也成等变式训练:差数列.3.通项公式法1242{}1lg,lg,lg,,{}nnnaaabnNabn.已知a是各项为不同的正数的等差数列,成等差数列,又证明:数列例3是等比数列.2{}2,{}nnnann已知数列a的前n项和为S求证变式:数列是训练:等差数列.4.前n项和公式法2{}9,58,_____.__.4nnkanSnnkak已知数列的前项和第项满足则例{}lg(1),{}nnSnnnn:数列a的前项和为S,且则数列a是_______变式训练_数列?1.已知函数f(x)=(x-1)2,g(x)=4(x-1),数列{an}满足a1=2,(an+1-an)g(an)+f(an)=0.(1)用an表示an+1;(2)求证:{an-1}是等比数列.作业:22112.{}()(1)}2{}816,{}.nnnnnnnabaanZabanSn已知数列是等差数列,求证:数列{b是等差数列;()若数列的公差为,求数列的前项和113.}2,=431,.(1){}2{}.nnnnnnaaaannNananS在数列{中,证明数列是等比数列;()求数列的前项和