已知等差数列{an}的前几项和sn=63,a4=9,a9=-1,则n=?
人气：295 ℃ 时间：2020-03-20 13:01:32
解答
a4=a1+3d=9 (1) a9=a1+8d=-1 (2)
(2)-(1):5d=-10 d=-2 a1= -1+16=15
(a1+an)n=126
[15+15-2(n-1)]n=126
[30-2n+2]n=126
[32-2n]n=126
2n²-32n+126=0
n²-16n+63=0
(n-7)(n-9)=0
∴ n=7 or n=9
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