设等差数列an的前n项和为Sn,a1=3/2,且s1,s2,s4成等比数列,求sn

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设等差数列an的前n项和为Sn,a1=3/2,且s1,s2,s4成等比数列,求sn

设等差数列an的前n项和为Sn,a1=3/2,且s1,s2,s4成等比数列,求sn
设等差数列an的前n项和为Sn,a1=3/2,且s1,s2,s4成等比数列,求sn

设等差数列an的前n项和为Sn,a1=3/2,且s1,s2,s4成等比数列,求sn
s1,s2,s4成等比数列,则
2s2=s1+s4
即2a1+2a2=2a1+a2+a3+a4
a2=a3+a4
设等差数列通项公式为:an=a1+(n-1)d,

a1+d=2a1+5d
得d=-3/8
所以an=3/2+(n-1)(-3/8)=15/8-3n/8
所以sn=(a1+an)n/2
=(27/8-3n/8)n/2

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