等比数列前n项和为,Sn=3^n+k,则k=?

题目

等比数列前n项和为,Sn=3^n+k,则k=?

答案

Sn=(3^n)+k,S1=a1=3+k
Sn=a1(1-q^n)/(1-q)=3^n+k
所以q=3
Sn=a1(1-3^n)/(1-3)=-(a1)/2+3^n(a1)/2=3^n+k
(a1)/2=1,k=-(a1)/2,
所以a1=2,k=-1