设Sn是等差数列{an}的前n项和,且a5=7,Sn=1368,Sn-9=783,则n=______.-数学

题目简介

设Sn是等差数列{an}的前n项和,且a5=7,Sn=1368,Sn-9=783,则n=______.-数学

题目详情

设Sn是等差数列{an}的前n项和,且a5=7,Sn=1368,Sn-9=783,则n=______.
题型:填空题难度:中档来源:不详

答案

由题意可得S9=
9(a1+a9)
2
=
9×2a5
2
=9a5=63,
又Sn=1368,Sn-9=783,故Sn-Sn-9=585,
故S9+Sn-Sn-9=(a1+a2+…+a9)+(an+an-1+…+an-8)
=(a1+an)+(a2+an-1)+…+(a9+an-8)=9(a1+an)=585+63=648,
解得a1+an=72,由Sn=
n(a1+an)
2
=36n=1368,可得n=38,
故答案为:38

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