已知数列{An}的前n项的和Sn满足6Sn=An^2十3An十2,且An>0.1.求首项A1 2已知数列{An}的前n项的和Sn满足6Sn=An^2十3An十2,且An>0.1.求首项A12.证明{An}是等差数列.3,求通项公式An

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$已知数列{An}的前n项的和Sn满足6Sn=An^2十3An十2,且An>0.1.求首项A1 2已知数列{An}的前n项的和Sn满足6Sn=An^2十3An十2,且An>0.1.求首项A12.证明{An}是等差数列.3,求通项公式An$

已知数列{An}的前n项的和Sn满足6Sn=An^2十3An十2,且An>0.1.求首项A1 2已知数列{An}的前n项的和Sn满足6Sn=An^2十3An十2,且An>0.1.求首项A12.证明{An}是等差数列.3,求通项公式An
已知数列{An}的前n项的和Sn满足6Sn=An^2十3An十2,且An>0.1.求首项A1 2
已知数列{An}的前n项的和Sn满足6Sn=An^2十3An十2,且An>0.
1.求首项A1
2.证明{An}是等差数列.
3,求通项公式An

已知数列{An}的前n项的和Sn满足6Sn=An^2十3An十2,且An>0.1.求首项A1 2已知数列{An}的前n项的和Sn满足6Sn=An^2十3An十2,且An>0.1.求首项A12.证明{An}是等差数列.3,求通项公式An
(1)
6Sn=(an)^2+3an+2
n=1
6a1=(a1)^2+3a1+2
(a1)^2-3a1+2=0
(a1-1)(a1-2)=0
a1=1 or 2
(2)
an = Sn -S(n-1)
6an =(an)^2+3an-(a(n-1))^2-3a(n-1)
[an +a(n-1)].[an -a(n-1)-3]=0
an -a(n-1)-3 =0
an -a(n-1)=3
=>{an}}是等差数列, d=3
(3)
an - a1= 3(n-1)
an = 3n-2 or 3n-1

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