Question

已知数列{An}的各项均为正数,前n项和Sn满足6Sn=An^2+3An+2,若A2,A4,A9成等比数列,则数列{an

Answer 1

6Sn=An^2+3An+2

6S(n-1)=[A(n-1)]^2+3A(n-1)+2

6Sn-6S(n-1)=6An=An^2+3An+2-{[A(n-1)]^2+3A(n-1)+2}

An-A(n-1)=3

{An}为等差数列,d=3

A4^2=A2A9

A2=A1+d;A4=A1+3d;A9=A1+8d

分别代入得

A1=d/3=1

An=1+3(n-1)=3n-2