设等差数列{an}的前n项和为Sn,且S4=-62,S6=-75求{an}的通向公式an及前n项和Sn,求出前n项和的最小值

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设等差数列{an}的前n项和为Sn,且S4=-62,S6=-75求{an}的通向公式an及前n项和Sn,求出前n项和的最小值
设等差数列{an}的前n项和为Sn,且S4=-62,S6=-75
求{an}的通向公式an及前n项和Sn,求出前n项和的最小值

设等差数列{an}的前n项和为Sn,且S4=-62,S6=-75求{an}的通向公式an及前n项和Sn,求出前n项和的最小值
因为等差,故可设：
sn=An^2+Bn
S4=-62,S6=-75
-62=A4^2+4B
-75=A6^2+6B
解得：A=3/2
B=-43/2
故sn=3/2n^2-43n/2
而sn=na1+n(n-1)d/2
=d/2n^2+na1-dn/2
=d/2n^2+(a1-d/2)n
故d=2A=3
a1=d/2+B=20
an=20+(n-1)*3=3n+17
最小值：显然an是递增数列,当n=1时取最小值
a1=20

a2+a3=S4/2=-31
a5+a6=S6-S4=-13
所以d=3
a2=-17
a1=-20
an=a1

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