已知数列{an}满足an=3an-1+3n-1(n∈N*,n≥2),且a1=5,若bn=13n(an+t)(n∈N*)且{bn}的等差数列,则t=______.-数学

题目简介

已知数列{an}满足an=3an-1+3n-1(n∈N*,n≥2),且a1=5,若bn=13n(an+t)(n∈N*)且{bn}的等差数列,则t=______.-数学

题目详情

已知数列{an}满足an=3an-1+
3
-1(n∈N*,n≥2)
,且a1=5,若bn=
1
3
(an+t)(n∈N*)
且{bn}的等差数列,则t=______.
题型:填空题难度:偏易来源:不详

答案

当n≥2 时,bn-bn-1=class="stub"1
3n
(an+t)-class="stub"1
3n-1
(an-1+t)
∵an=3an-1+3n-1
∴bn-bn-1=1-class="stub"1+2t
3n

要使{bn} 为等差数列,则必需使1+2t=0,∴t=-class="stub"1
2

故答案为:-class="stub"1
2

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