合聚咖

合聚咖

请问第18题怎么写

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选择②补充到题目,即a5是a2和a6的等比中项,即a5/a2=a6/a5

由Sn=nan+n(n-1),可知:

S1=a1,S2=2a2+2,S3=3a3+6,S4=4a4+12,...

a2=S2-S1=2a2+2-a1,a1=a2+2,

a3=S3-S2=3a3+6-2a2-2,2a2=2a3+4,

a2=a3+2

a4=S4-S3=4a4+12-3a3-6,3a3=3a4+6,

a3=a4+2

所以,数列为: a1,a1-2,a1-4,a1-6,...,a1-2(n-1),...

a2=a1-2,a5=a1-8,a6=a1-10

因为 a5/a2=a6/a5,所以

(a1-8)/(a1-2)=(a1-10)/(a1-8)

(a1)^2-16a1+64=(a1)^2-12a1+20

4a1=44,所以a1=11

数列是:a0=0,11,9,7,5,3,1,-1,-3,...

S0=0,S1=11,S2=20,...,Sn,...

所以,在S0,S1,S2,S3,...,Sn,...中最大值是S6=36