等差数列an中,(a3,a7,a10)为等比数列,a1=1则s5=?

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等差数列an中,(a3,a7,a10)为等比数列,a1=1则s5=?

等差数列an中,(a3,a7,a10)为等比数列,a1=1则s5=?
等差数列an中,(a3,a7,a10)为等比数列,a1=1则s5=?

等差数列an中,(a3,a7,a10)为等比数列,a1=1则s5=?
设公差为d,a3=a1+2d=1+2d,a7=a1+6d=1+6d,a10=a1+9d=1+9d
∵a3,a7,a10成等比数列
∴a7^2=a3×a10
即(1+6d)^2=(1+2d)×(1+9d)
1+12d+36d^2=1+11d+18d^2
18d^2+d=0
d(18d+1)=0
d=0或d=-1/18
当d=0时
S5=na1=5×1=5
当d=-1/18时
Sn=na1+n(n-1)d/2
=5×1+5×4×(-1/18)/2
=5-5/9
=40/9

设公差为m
a3=1+2m a7=1+6m a10=1+9m
a3,a7,a10为等比数列,则
a3*a10= a7^2
(1+2m)*(1+9m)=(1+6m)^2
18m^2+11m+1=36m^2+12m+1
18m^2+m=0
18m(m+1)=0
m=0或m=-1
m=0时
S5=5
m=-1时
S5=1+0-1-2-3=-5
思路就是这样可能有计算错误,最好你自己检查一下