已知等差数列an'的公差d=1,前n项和为Sn（1）若1,a1,a3成等比数列,求a1（2）若S5＞a1a9,求a的取值

Question

已知等差数列an'的公差d=1,前n项和为Sn （1）若1,a1,a3成等比数列,求a1
（2）若S5＞a1a9,求a的取值

Answer 1

第一问
1,a1,a3成等比数列
a1^2=1*a3
a1^2=a1+2d=a1+2
a1^2-a1-2=0
(a1-2)(a1+1)=0
a1=2或a1=-1
(2)
S5=a1a9
5a1+5*4/2*1=a1*(a1+8)
5a1+10=a1^2+8a1
a1^2+3a1-10=0
(a1+5)(a1-2)=0
a1=-5或a1=2
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