已知等差数列{an},{bn}的前n项和为Sn,Tn,若对于任意的自然数n,都有SnTn=2n+33n+6,则a7b5+b7+a3b4+b8=______.-数学

题目简介

已知等差数列{an},{bn}的前n项和为Sn,Tn,若对于任意的自然数n,都有SnTn=2n+33n+6,则a7b5+b7+a3b4+b8=______.-数学

题目详情

已知等差数列{an},{bn}的前 n 项和为Sn,Tn,若对于任意的自然数n,都有
Sn
Tn
=
2n+3
3n+6
,则
a7
b5+b7
+
a3
b4+b8
=______.
题型:填空题难度:中档来源:不详

答案

∵等差数列{an},{bn}的前 n 项和为Sn,Tn,
对于任意的自然数n,都有
Sn
Tn
=class="stub"2n+3
3n+6

a7
b5+b7
+
a5
b4+b8
=
a7
2b6
+
a5
2b6

=
2a6
2b6

=
a1+a11
b1+b11

=
S11
T11

=class="stub"2×11+3
3×11+6

=class="stub"25
39

故答案为:class="stub"25
39

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