已知正项等差数{an}的前n项和为Sn,若S3=12,且2a1,a2,a3+1成等比数列,记bn=an/3^n的前n项和为Tn,求T

题目

已知正项等差数{an}的前n项和为Sn,若S3=12,且2a1,a2,a3+1成等比数列,记bn=an/3^n的前n项和为Tn,求T

答案

S3=a1+a2+a3=a1+a1+d+a1+2d=3(a1+d)=12a1+d=4=a2(a2)^2=2a1*(a3+1)16=2a1*(a1+2d+1) a1+d=4联合方程解得 a1=8（舍去）a1=1 d=3bn-b(n-1)=an/(3^n)-a(n-1)/3^(n-1)=an/(3^n)-3a(n-1)/(3^n)=[an-3a(n-1)]/(3^n)=[an-a(...