.已知Sn是等差数列{an}的前n项和,若S6=36,Sn=324,Sn-6=144(n>6),则n等于 ()

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.已知Sn是等差数列{an}的前n项和,若S6=36,Sn=324,Sn-6=144(n>6),则n等于().已知Sn是等差数列{an}的前n项和,若S6=36,Sn=324,Sn-6=144(n>6

.已知Sn是等差数列{an}的前n项和,若S6=36,Sn=324,Sn-6=144(n>6),则n等于 ()
.已知Sn是等差数列{an}的前n项和,若S6=36,Sn=324,Sn-6=144(n>6),则n等于 ()

.已知Sn是等差数列{an}的前n项和,若S6=36,Sn=324,Sn-6=144(n>6),则n等于 ()
S(n-6)-S6
=a7+a8+.+a(n-6)
=[a7+a(n-6)]*(n-12)/2
=[a1+a(n)]*(n-12)/2=108 (1)
Sn=a1+a2+.+a(n)
=[a1+a(n)]*n/2=324 (2)
(1)÷(2)
(n-12)/n=108/324=1/3
n=3n-36
n=18

由已知条件得:
S6:S(n-6):Sn=36:144:324=1:4:9
即 S6:[S(n-6)-S6]:[Sn-S(n-6)]=1:3:5
故可知6,n-6,n三项也成等差数列
所以2(n-6)=n6
n=18