等差数列{an}中,Sn=18,an+an-1+an-2=3,S3=1n=?

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等差数列{an}中,Sn=18,an+an-1+an-2=3,S3=1n=?等差数列{an}中,Sn=18,an+an-1+an-2=3,S3=1n=?等差数列{an}中,Sn=18,an+an-1+

等差数列{an}中,Sn=18,an+an-1+an-2=3,S3=1n=?
等差数列{an}中,Sn=18,an+an-1+an-2=3,S3=1
n=?

等差数列{an}中,Sn=18,an+an-1+an-2=3,S3=1n=?
设an=a+(n-1)d
Sn=[a+a+(n-1)d]xn/2=[2a+(n-1)d]xn/2=18
an+an-1+an-2=a+(n-1)d+a+(n-2)d+a+(n-3)d=3a+(3n-6)d=3
S3=a+a+d+a+2d=3a+3d=1
由3a+(3n-6)d=3和3a+3d=1解得
a=(n-5)/(3n-9) d=2/(3n-9)
将a、d代入[2a+(n-1)d]xn/2=18
[(2n-10)/(3n-9)+(2n-2)/(3n-9)]xn/2=18
[(4n-12)/(3n-9)]xn/2=18
4/3xn/2=18
n=27

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