数列{an}中,a3=2,a7=1,且数列{1an+1}是等差数列,则a11=______.-数学

题目简介

数列{an}中,a3=2,a7=1,且数列{1an+1}是等差数列,则a11=______.-数学

题目详情

数列{an}中,a3=2,a7=1,且数列{
1
an+1
}是等差数列,则a11=______.
题型:填空题难度:偏易来源:武昌区模拟

答案

∵数列{class="stub"1
an+1
}是等差数列,class="stub"1
a3+1
=class="stub"1
3
class="stub"1
a7+1
=class="stub"1
2
,且 class="stub"1
a3+1
+class="stub"1
a11+1
=class="stub"2
a7+1

class="stub"1
3
+class="stub"1
a11+1
=1,∴class="stub"1
a11+1
=class="stub"2
3
,∴a11 +1=class="stub"3
2
,∴a11=class="stub"1
2

故答案为:class="stub"1
2

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