设等差数列{an}的前n项和为Sn,且a3+a7-a10=8,a11-a4=4,则S13等于?

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设等差数列{an}的前n项和为Sn,且a3+a7-a10=8,a11-a4=4,则S13等于?设等差数列{an}的前n项和为Sn,且a3+a7-a10=8,a11-a4=4,则S13等于?设等差数列{

设等差数列{an}的前n项和为Sn,且a3+a7-a10=8,a11-a4=4,则S13等于?
设等差数列{an}的前n项和为Sn,且a3+a7-a10=8,a11-a4=4,则S13等于?

设等差数列{an}的前n项和为Sn,且a3+a7-a10=8,a11-a4=4,则S13等于?
方法1:设公差为d,
a3+a7-a10=a1+2d+a1+6d-(a1+9d)=2a1-d=8
a11-a4=a1+10d-(a1+3d)=7d=4
d=4/7
a1=60/7
a13=a1+12d=108/7
S13=(a1+a13)×13/2=156
方法2:两式相加:a3+a7-a10+a11-a4=12
a7+(a3-a4)-(a10-a11)=12
因为a3-a4=a10-a11=-d
因此结果为a7.
所以a7=12
S13=a1+a13+a2+a12+a3+a11+...+a7
因为a1+a13=a2+a12=a3+a11=...=2a7
所以S13=13a7=156
不好意思,刚才口算错误

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