已知数列{an}的前n项和为Sn,a1=3且an+1=2Sn+3,数列{bn}为等差数列,且公差d>0,b1+b2+b3=15; (1)求数列{an}的通项公式; (2)若a13+b1,a23+b2,a33+b3成等比数列,求数列{bn}的
问题描述:
已知数列{an}的前n项和为Sn,a1=3且an+1=2Sn+3,数列{bn}为等差数列,且公差d>0,b1+b2+b3=15;
(1)求数列{an}的通项公式;
(2)若
+b1,a1 3
+b2,a2 3
+b3成等比数列,求数列{bn}的前项和Tn. a3 3
答
(1)由an+1=2Sn+3,得an=2sn-1+3(n≥2)(2分)相减得:an+1-an=2(Sn-Sn-1),即an+1-an=2an,则an+1an=3(4分)∵当n=1时,a2=2a1+3=9,∴a2a1=3(5分)∴数列{an}是等比数列,∴an=3•3n-1=3n(6分)(2)∵b...