等差数列{an}中,前n项和为Sn,若S3=21,S8=136,则Sn=?

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等差数列{an}中,前n项和为Sn,若S3=21,S8=136,则Sn=?等差数列{an}中,前n项和为Sn,若S3=21,S8=136,则Sn=?等差数列{an}中,前n项和为Sn,若S3=21,S

等差数列{an}中,前n项和为Sn,若S3=21,S8=136,则Sn=?
等差数列{an}中,前n项和为Sn,若S3=21,S8=136,则Sn=?

等差数列{an}中,前n项和为Sn,若S3=21,S8=136,则Sn=?
直接来s3=3*a1+3d=21
s8=8*a1+8*7/2*d=8*a1+28d=136
解方程得d=4
a1=3
sn=a1*n+n*(n-1)/2*d
=2n^2+n

S3=21
a1+a2+a3=21
a2=7
S8=136
S8=8(a1+a8)/2=4(a2+a7)=4(7+a7)=136
a7=27
d=(a7-a2)/5=(27-7)/5=4
a1=a2-d=7-4=3,an=a1+(n-1)d=3+4(n-1)=4n-1
所以Sn=n(a1+an)/2=n(3+4n-1)/2=n(2n+1)

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