等差数列{an}中,已知an=3n-1,若数列{1anan+1}的前n项和为425,则n的值为()A.13B.14C.15D.16-数学

题目简介

等差数列{an}中,已知an=3n-1,若数列{1anan+1}的前n项和为425,则n的值为()A.13B.14C.15D.16-数学

题目详情

等差数列{an}中,已知an=3n-1,若数列{
1
anan+1
}的前n项和为
4
25
,则n的值为(  )
A.13B.14C.15D.16
题型:单选题难度:偏易来源:不详

答案

∵an=3n-1,
class="stub"1
anan+1
=class="stub"1
(3n-1)(3n+2)
=class="stub"1
3
(class="stub"1
3n-1
-class="stub"1
3n+2
)

∵数列{class="stub"1
anan+1
}的前n项和为class="stub"4
25

∴Sn=class="stub"1
3
(class="stub"1
2
-class="stub"1
5
)
+class="stub"1
3
(class="stub"1
5
-class="stub"1
8
)
+class="stub"1
3
(class="stub"1
8
-class="stub"1
11
)
+…+class="stub"1
3
(class="stub"1
3n-1
-class="stub"1
3n+2
)

=class="stub"1
3
(class="stub"1
2
-class="stub"1
3n+2
)
=class="stub"4
25

解得n=16.
故选D.

更多内容推荐