已知等差数列{an}中,a1=-60,an+1=an+3,求Sn=|a1|+|a2|+…+|an|
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![已知等差数列{an}中,a1=-60,an+1=an+3,求Sn=|a1|+|a2|+…+|an|](/uploads/image/z/1094005-37-5.jpg?t=%E5%B7%B2%E7%9F%A5%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97%7Ban%7D%E4%B8%AD%2Ca1%3D-60%2Can%2B1%3Dan%2B3%2C%E6%B1%82Sn%3D%7Ca1%7C%2B%7Ca2%7C%2B%E2%80%A6%2B%7Can%7C)
已知等差数列{an}中,a1=-60,an+1=an+3,求Sn=|a1|+|a2|+…+|an|
已知等差数列{an}中,a1=-60,an+1=an+3,求Sn=|a1|+|a2|+…+|an|
已知等差数列{an}中,a1=-60,an+1=an+3,求Sn=|a1|+|a2|+…+|an|
等差数列的公差为3
an=-60+3(n-1)=3n-63
an>0,则3n-63>0
∴ n>21
(1) n≤21
Sn=|a1|+|a2|+…+|an|
=-(a1+a2+.+an)
=-(-60+3n-63)*n/2
=(-3n²+123n)/2
S21=-(-60+0)*21/2=630
(2)n>21
Sn=|a1|+|a2|+…+|an|
=-(a1+a2+.+a21)+(a22+a23+.+an)
=-2(a1+a2+.+a21)+(a1+a2+.+an)
=2S21+(-60+3n-63)*n/2
=1260+(3n²-123n)/2
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