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若两个等差数列{an}和{bn}的前n项和分别是Sn,Tn,已知SnTn=7nn+3,则a10b9+b12+a11b8+b13=.

题目详情
若两个等差数列{an}和{bn}的前n项和分别是Sn,Tn,已知
Sn
Tn
=
7n
n+3
,则
a10
b9+b12
+
a11
b8+b13
=___.
▼优质解答
答案和解析
∵数列{an}和{bn}都是等差数列,
a10
b9+b12
+
a11
b8+b13
=
a10+a11
b9+b12
=
a10+a11
b10+b11
=
S20
T20
=
7×20
20+3
=
140
23

故答案是:
140
23