求Sn最大值等差数列{a(n)}中,a(1)=25,S(9)=S(17),则Sn的最大值为_____________答案

a(1)=25
a(9)=a(1)+8d=25+8d
s(9)=[a(1)+a(9)]*9/2=(25+4d)*9
a(17)=a(1)+16d=25+16d
s(17)=[a(1)+a(17)]*17/2=(25+8d)*17
(25+4d)*9=(25+8d)*17
d=-2
a(n)=a(1)+(n-1)d=25-2(n-1)=27-2n
s(n)=[a(1)+a(n)]*n/2=(25+27-2n)*n/2
=(26-n)*n
=-n^2+26n
=-(n-13)^2+169
n=13时sn有最大值169