等差数列{an}中,S10=100,S100=10,求 S110

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等差数列{an}中,S10=100,S100=10,求 S110
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等差数列{an}中,S10=100,S100=10,求 S110
等差数列{an}中,S10=100,S100=10,求 S110

等差数列{an}中,S10=100,S100=10,求 S110
因为等差,假设a1=a,公差d,则有an=a+(n-1)d
s10=(a1+a10)*10/2
=(2a+9d)*5
=10a+45d=100
s100=(a1+a100)*100/2
=(2a+99d)*50
=100a+4950d=10
s110=(a1+a110)*110/2
=(2a+109d)*55
=110a+5995d
s100-s10*10
=4500d=-990
d=-0.22
s110=s10+s100+1000d=100+10-220=-110