Question

数列{An}的前n项和为Sn.Sn=2An-3n.(n属于整N).若{An+c}成等比数列,求常数c.

Answer 1

Sn=2An-3n

S(n-1)=2A(n-1)-3(n-1)

相减

Sn-S(n-1)=An

所以An=2An-2A(n-1)-3

An=2A(n-1)+3

An+c=2A(n-1)+3+c=2[A(n-1)+3/2+c/2]

(An+c)/[A(n-1)+3/2+c/2]=2

是等比数列则c=3/2+c/2

c=3