数列{an} 满足a1=1 3(a1+a2+a3+,,,,an)=(n+2)an求通项an

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3(a1+a2+a3+,,,,an)=(n+2)an
3Sn=(n+2)an
3S(n-1)=(n+1)a(n-1) 相燃历减
3an=(n+2)an-(n+1)a(n-1)
(n-1)an=(n+1)a(n-1)
an/a(n-1)=(n+1)/虚搏(n-1)
a2/a1=3/1
a3/a2=4/2
a4/a3=5/皮誉搜3
……
an/a(n-1)=(n+1)/(n-1) 叠乘
an/a1=n(n+1)/2 a1=1
an=n(n+1)/2

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