专题突破练14求数列的通项及前n项和1.(2023江西宜春高三上学期期末)已知等差数列{an}的前n项和为Sn,且a2+a6=10,S5=20.(1)求an与Sn;(2)设数列{cn}满足cn=1Sn-n,求{cn}的前n项和Tn.2.(2023吉林高中高三上学期期末考试)在递增的等比数列{an}中,a2=6,且4(a3-a2)=a4-6.(1)求{an}的通项公式;(2)若bn=an+2n-1,求数列{bn}的前n项和Sn.13.已知数列{an}满足a1=12,an+1=an2an+1.(1)证明数列{1an}是等差数列,并求{an}的通项公式;(2)若数列{bn}满足bn=12n·an,求数列{bn}的前n项和Sn.4.(2023辽宁朝阳重点高中高三第四次模拟)已知等差数列{an}的前n项和为Sn,满足S3=12,且a1,a2,a4成等比数列.(1)求an及Sn;2(2)设bn=Sn·2ann,数列{bn}的前n项和为Tn,求Tn.35.已知数列{an}满足a1=1,a2=3,an+2=3an+1-2an(n∈N*).(1)证明:数列{an+1-an...
