If the tolerance D of the arithmetic sequence (an) is not equal to 0, and A1 and A2 are two of the equations X & # 178; - a3x + A4 = 0 about X, then the general term formula of (an) is

If the tolerance D of the arithmetic sequence (an) is not equal to 0, and A1 and A2 are two of the equations X & # 178; - a3x + A4 = 0 about X, then the general term formula of (an) is

x²-a3x +a4＝0
a1+a2=a3
a1+a1+d=a1+2d
a1=d
a1*a2=a4
a1(a1+d)=a1+3d
2d²=4d
2d(d-2)=0
We get d = 2
So A1 = D = 2
an=2+2(n-1)=2n

If {an} is known to be an arithmetic sequence and the tolerance D ≠ 0, A1 and A2 are the two roots of the equation x2-a3x + A4 = 0 about X, then an}=______ ．

∵ {an} is an arithmetic sequence, and the tolerance D ≠ 0, A1, A2 are the two roots of the equation x2-a3x + A4 = 0 about X, ∵ a1 + A2 = A3, A1 · A2 = A4. That is, 2A1 + D = a1 + 2D, A1 · (a1 + D) = (a1 + 3D), the solution is A1 = D = 2, ∵ an = 2 + (n-1) · 2 = 2n, so the answer is 2n

Given the arithmetic sequence an, tolerance is greater than zero, A2, A5 are two of the equations x ^ 2-12x + 27 = 0, the sum of the first n terms of the other sequence is Sn, and Sn = 1-bn / 2
N belongs to a positive integer. Note CN = an * BN (n belongs to a positive integer). (1) find the general term formula of an and BN respectively. (2) try to find the maximum term of the sequence CN. If cn is less than or equal to m ^ 2-2m + 2 / 3 and holds for all natural numbers n, find the value range of real number M

1. Using the root formula of bivariate linear equation, two of them are obtained: 9, 3 and an are arithmetic sequence, and the tolerance is greater than zero, so A2 = 3, A5 = 9 and A5 = A3 + 2D, so 2D = a5-a3 = 9-3 = 6, d = 3 and A3 = a1 + 2D, A1 = a3-2d = 3-6 = - 3, so an = a1 + (n-1) d = - 3 + (n-1) * 3 = 3n-6 (n is a positive integer) s