a1=1,a(n+1)=6n-an,求an
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a1=1,a(n+1)=6n-an,求ana1=1,a(n+1)=6n-an,求ana1=1,a(n+1)=6n-an,求an因为a(n+1)=6n-an所以a(n+1)-3n=-(an-3n)所以a
a1=1,a(n+1)=6n-an,求an
a1=1,a(n+1)=6n-an,求an
a1=1,a(n+1)=6n-an,求an
因为 a(n+1) = 6n-an
所以 a(n+1)-3n = -(an-3n)
所以 a(n+1)-3n-3 = -(an-3n)-3
所以 a(n+1)-3(n+1) = -(an-3n)-3
所以 a(n+1)-3(n+1) = -(an-3n)-3
所以 a(n+1)-3(n+1) = -[(an-3n)+1.5]-1.5
所以 a(n+1)-3(n+1)+1.5 = -[(an-3n)+1.5]
设[(an-3n)+1.5]为bn
所以 a(n+1)-3(n+1)+1.5 = -[(an-3n)+1.5] 可化为 b(n+1)=-bn
所以 b(n+1)/bn = -1
所以 b(n+1)/bn = -1, b(n)/b(n-1) = -1, …… b2/b1=-1
把上面的n个式子乘起来,有b(n+1)/b1 = (-1)^n
所以 b(n) = (-1)^(n-1)*b1 , b1=a1-3+1.5 = -0.5
所以 [(an-3n)+1.5] = (-1)^(n-1)*(-0.5) =0.5(-1)^n
所以 an= 0.5(-1)^n+3n-1.5
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