等差数列{an}中,a3=8,a7=20,若数列{1anan+1}的前n项和为425,则n的值为()A.14B.15C.16D.18-数学

题目简介

等差数列{an}中,a3=8,a7=20,若数列{1anan+1}的前n项和为425,则n的值为()A.14B.15C.16D.18-数学

题目详情

等差数列{an}中,a3=8,a7=20,若数列{
1
anan+1
}的前n项和为
4
25
,则n的值为(  )
A.14B.15C.16D.18
题型:单选题难度:偏易来源:不详

答案

设等差数列的首项为a,公差为d,
因为a3=8,a7=20,所以a+2d=8,a+6d=20,解得a=3,a=2.an=3n-1;
又因为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
),
所以Sn=class="stub"1
3
class="stub"1
2
-class="stub"1
5
+class="stub"1
5
-class="stub"1
8
+class="stub"1
8
-class="stub"1
11
+…+class="stub"1
3n-1
-class="stub"1
3n+1

=class="stub"1
3
class="stub"1
2
-class="stub"1
3n+1
)=25,解得n=16
故选C

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