公差不为零的等差数列an的前n项和为sn 若a4是a3与a7的等比中项 s8等于32 则s10等于

Question

如题所述

Answer 1

a4=a3+d a7=a3+4d
(a4)²=（a3）（a7）
(a3+d)²=(a3)(a3+4d)
d≠0, 解得a4=3d/2
a1=a4-3d=-3d/2
Sn=a1n+n(n-1)d/2=-3nd/2+n(n-1)/2=n(n-4)d/2
S8=8(8-4)d/2=16d=32
∴d=2, Sn=n(n-4)
S10=10(10-4)=60

Answer 2

a4�0�5=a3a7=(a4-d)(a4+3d)
∴a4�0�5=a4�0�5-3d�0�5+2da4
d≠0, 解得a4=3d/2
a1=a4-3d=-3d/2
Sn=a1n+n(n-1)d/2=-3nd/2+n(n-1)/2=n(n-4)d/2
S8=8(8-4)d/2=16d=32
∴d=2, Sn=n(n-4)
S10=10(10-4)=60