9、在数列{an}中,an≠0,a1,a2,a3成等差数列,a2,a3,a4成等比数列,a3,a4,a5的倒数成等差数列,则a1,a3,a5( )A．是等差数列 B．是等比数列C．的倒数成等差数列 D．的平方成等差数列

9、在数列{an}中,an≠0,a1,a2,a3成等差数列,a2,a3,a4成等比数列,a3,a4,a5的倒数成等差数列,则a1,a3,a5( )A．是等差数列 B．是等比数列C．的倒数成等差数列 D．的平方成等差数列
9、在数列{an}中,an≠0,a1,a2,a3成等差数列,a2,a3,a4成等比数列,a3,a4,a5的倒数成等差数列,则a1,a3,a5( )
A．是等差数列 B．是等比数列
C．的倒数成等差数列 D．的平方成等差数列

9、在数列{an}中,an≠0,a1,a2,a3成等差数列,a2,a3,a4成等比数列,a3,a4,a5的倒数成等差数列,则a1,a3,a5( )A．是等差数列 B．是等比数列C．的倒数成等差数列 D．的平方成等差数列
2a2=a1+a3 (1)
(a3)^2=a2*a4 (2)
2/a4=1/a3+1/a5 (3)
由(1)得a2=(a1+a3)/2 (4)
由(3)得a4=2a3*a5/(a3+a5) (5)
将(4)(5)代入(2)
(a3)^2=(a1+a3)/2 * 2a3*a5/(a3+a5)
a3=(a1+a3)/2* 2a5/(a3+a5)
(a3)^2+a3*a5=a1*a5+a3*a5
(a3)^2=a1*a5
故答案B正确

应该是等比数列 选B
根据题意,有2*a2=a1+a3,即a2=(a1+a3)/2 a3^2=a2*a4
a4=2a3*a5/(a3+a5)
把a2=(a1+a3)/2和a4=2a3*a5/(a3+a5) 代入a3^2=a2*a4
得到a1，a3，a5的关系a3^2=a1*a5 即a1，a3，a5成等比数列