Question

设数列{an}的前n项和为Sn,且Sn=2an-3(n=1,2,…).

设数列{an}的前n项和为Sn，且Sn=2an-3（n=1，2，…）．
1.求an。2.bn=an+2n，求bn和

Answer 1

Answer 2

1. Sn=2an-3，Sn-1=2a(n-1)-3

   Sn-Sn-1=an=2[an-a(n-1)],an=2a(n-1)

   所以an是公比为2的等比数列。S1=a1=2a1-3,a1=3

   an=3*2^(n-1)

2. bn=an+2n令bn的和为Tn

   Tn=3*(1-2^n)/(1-2)+(2+2n)*n/2

       =3*2^n-3+n2+n