设等差数列{an}、{bn}的前n项和分别为Sn、Tn,若对任意自然数n都有SnTn=2n-34n-3,则a9b5+b7+a3b8+b4的值为______.-数学

题目简介

设等差数列{an}、{bn}的前n项和分别为Sn、Tn,若对任意自然数n都有SnTn=2n-34n-3,则a9b5+b7+a3b8+b4的值为______.-数学

题目详情

设等差数列{an}、{bn}的前n项和分别为Sn、Tn,若对任意自然数n都有
Sn
Tn
=
2n-3
4n-3
,则
a9
b5+b7
+
a3
b8+b4
的值为 ______.
题型:填空题难度:偏易来源:江苏模拟

答案

∵{an},{bn}为等差数列,
a9
b5+b7
+
a3
b8+b4
=
a9
2b6
+
a3
2b6
=
a9+a3
2b6
=
2a6
2b6

S11
T11
=
a1+a11
b1+b11
=
2a6
2b6
=class="stub"2×11-3
4×11-3
=class="stub"19
41

a9
b5+b7
+
a3
b8+b4
=class="stub"19
41

故答案为class="stub"19
41

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