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

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

6S1=6A1=A1^2+3A1+2

A1^2-3A1+2=0

A1=1或2

An=1+3(n-1)=3n-2 或3n-1