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
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![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](/uploads/image/z/729960-24-0.jpg?t=9%E3%80%81%E5%9C%A8%E6%95%B0%E5%88%97%7Ban%7D%E4%B8%AD%2Can%E2%89%A00%2Ca1%2Ca2%2Ca3%E6%88%90%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97%2Ca2%2Ca3%2Ca4%E6%88%90%E7%AD%89%E6%AF%94%E6%95%B0%E5%88%97%2Ca3%2Ca4%2Ca5%E7%9A%84%E5%80%92%E6%95%B0%E6%88%90%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97%2C%E5%88%99a1%2Ca3%2Ca5%28+%29A%EF%BC%8E%E6%98%AF%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97+B%EF%BC%8E%E6%98%AF%E7%AD%89%E6%AF%94%E6%95%B0%E5%88%97C%EF%BC%8E%E7%9A%84%E5%80%92%E6%95%B0%E6%88%90%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97+D%EF%BC%8E%E7%9A%84%E5%B9%B3%E6%96%B9%E6%88%90%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97)
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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