设Sn是等差数列{an}的前n项和,已知S6=36,Sn=324,Sn-6=144,则n=()A.15B.16C.17D.18-数学

题目简介

设Sn是等差数列{an}的前n项和,已知S6=36,Sn=324,Sn-6=144,则n=()A.15B.16C.17D.18-数学

题目详情

设Sn是等差数列{an}的前n项和,已知S6=36,Sn=324,Sn-6=144,则n=(  )
A.15B.16C.17D.18
题型:单选题难度:中档来源:不详

答案

∵Sn=324,Sn-6=144,
∴Sn-Sn-6=an-5+an-4+…+an=180
又∵S6=a1+a2+…+a6=36,a1+an=a2+an-1=a6+an-5,
∴6(a1+an)=36+180=216
∴a1+an=36,由Sn=
(a1+an)n
2
=18n=324

∴n=18
故选D

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