> 数学 >
若数列{an}是等差数列,前n项和为Sn
a5
a3
5
9
,则
S9
S5
=______.
人气:285 ℃ 时间:2020-09-10 04:22:16
解答
由等差数列的求和公式可得:
S9
S5
=
9(a1+a9)
2
5(a1+a5)
2
=
9
5
a1+9
a1+5

由等差数列的性质可得:a1+a9=2a5,a1+a5=2a3
9
5
a1+9
a1+5
=
9
5
2a5
2a3
=
9
5
a5
a3
9
5
5
9
=1
故答案为:1
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