等差数列{an}的前n项和为Sn,公差d不等于0,且S3=9,a1,a3,a7成等比数列.(1)求数列{an}的通项公式(2)设bn=2^an,求数列{bn}的前n项和
S3=9
S3=a1+a2+a3=3a1+3d=9
a1+d=3=a2
a7=a1+6d=3+5d
a3=a2+d=3+d
a1=3-d
,a1,a3,a7成等比数列
a3^2=a1*a7
(3+d)^2=(3-d)(3+5d)
d^2-d=0
d=1
a1=3-1=2
an=a1+(n-1)d=2+(n-1)*1=2+n-1=n+1
b1=2^a1=2^2
b2=2^3
b3=2^4
b^n=2^(n+1)
Sn=2^2+2^3+2^4+...2^(n+1)
2Sn=2^3+2^4+...2^(n+1)+2^(n+2)
2Sn-Sn=2^(n+2)-2^2
Sn=2^(n+2)-4为啥不快个几十分钟T T30分钟完了吗？