Question

高中数学 高手速来要过程

已知等差数列an a2 a4 a9成等比数列 求（a1+a3+a5/a2+a4+a6 我知道是1/d 但d怎么算啊啊

Answer 1

a1+a3+a5/a2+a4+a6=3a3/3a4=a3/a4

因为
a2 a4 a9成等比数列
所以
a4²=a2a9
a4²=(a4-2d)(a4+5d)=a4²+3da4-10d²
3da4=10d²
1. d=0
a1+a3+a5/a2+a4+a6=1
2.d≠0
a4=10d/3
a3=a4-d=7d/3
所以
a3/a4=7/10

Answer 2

a4²=a2a9
(a1+3d)²=(a1+d)(a1+8d)
a1²+6a1d+9d²=a1²+9a1d+8d²
3a1d=d²
d=3a1

原式=(a1+a1+2d+a1+4d)/(a1+d+a1+3d+a1+5d)
=(3a1+6d)/(3a1+9d)
=(a1+6a1)/(a1+9a1)
=7/10

Answer 3

(a4)^2=a2*a9
(a1+3d)^2=(a1+d)*(a1+8d)
得到：d(3a1-d)=0
d=0或者d=3a1
d=0时，an=a1，所以a1+a3+a5/a2+a4+a6 =1
d=3a1时，a1+a3+a5/a2+a4+a6 =(3a1+6d)/(3a1+9d)=21d/30d=7/10

Answer 4

a3/a4
a2 (a2+2d),(a2+7d)等比（a2)*(a2+7d)=(a2+2d)^2打开后化简得
a2=(4d)/3
a3=(7d)/3
a4=(10d)/3
原式=(3*a2)/(3*a4)=7/10

Answer 5

成等比
a4&2=a2*a9
等差数列
(a1+3d)&2=(a1+d)(a1+8d)
d&2=3a1d
d=3a1
(a1+a3+a5)/(a2+a4+a6)
=3a3/3a4
=a3/a4=(a1+6a1)/(a1+9a1)
=7/10

Answer 6

通过a2,a4,a9等比，有(a1+d)(a1+8d)=(a1+3d)(a1+3d)，可以解出a1与d的关系然后把所求的式子都换成d或者a1，就可以了。。应该是，懒得算了