等比数列{an}的各项都是正数,且a2,12a3,a1成等差数列,则a4+a5a5+a6的值是()A.5-12B.1-52C.5+12D.5-12或5+12-数学

题目简介

等比数列{an}的各项都是正数,且a2,12a3,a1成等差数列,则a4+a5a5+a6的值是()A.5-12B.1-52C.5+12D.5-12或5+12-数学

题目详情

等比数列{an}的各项都是正数,且a2
1
2
a3,a1成等差数列,则
a4+a5
a5+a6
的值是(  )
A.
5
-1
2
B.
1-
5
2
C.
5
+1
2
D.
5
-1
2
5
+1
2
题型:单选题难度:偏易来源:不详

答案

设公比等于q,由题意可得 2×class="stub"1
2
a3=a2 +a1 ,即 a1 q2=a1 q+a1,解得 q=
5
+1
2

a4+a5
a5+a6
=
a4+a5
a4q+a5q
=class="stub"1
q
=class="stub"2
5
+1
=
2(
5
-1)
(
5
+1)(
5
-1)
=
5
-1
2

故选A.

更多内容推荐