The 38th term in the sequence is -51
Answer:
Estimate: 700 Answer: 712
Answer:

Step-by-step explanation:
we know that
The <u><em>conjugate root theorem</em></u> states that if the complex number a + bi is a root of a polynomial P(x) in one variable with real coefficients, then the complex conjugate a - bi is also a root of that polynomial
In this problem we have that
The polynomial has roots 1 and (1+i)
so
by the conjugate root theorem
(1-i) is also a root of the polynomial
therefore
The lowest degree of the polynomial is 3
so

Remember that
The leading coefficient is 1
so
a=1
![f(x)=(x-1)(x-(1+i))(x-(1-i))\\\\f(x)=(x-1)[x^{2} -(1-i)x-(1+i)x+(1-i^2)]\\\\f(x)=(x-1)[x^{2} -x+xi-x-xi+2]\\\\f(x)=(x-1)[x^{2} -2x+2]\\\\f(x)=x^{3}-2x^{2} +2x-x^{2} +2x-2\\\\f(x)=x^{3}-3x^{2} +4x-2](https://tex.z-dn.net/?f=f%28x%29%3D%28x-1%29%28x-%281%2Bi%29%29%28x-%281-i%29%29%5C%5C%5C%5Cf%28x%29%3D%28x-1%29%5Bx%5E%7B2%7D%20-%281-i%29x-%281%2Bi%29x%2B%281-i%5E2%29%5D%5C%5C%5C%5Cf%28x%29%3D%28x-1%29%5Bx%5E%7B2%7D%20-x%2Bxi-x-xi%2B2%5D%5C%5C%5C%5Cf%28x%29%3D%28x-1%29%5Bx%5E%7B2%7D%20-2x%2B2%5D%5C%5C%5C%5Cf%28x%29%3Dx%5E%7B3%7D-2x%5E%7B2%7D%20%2B2x-x%5E%7B2%7D%20%2B2x-2%5C%5C%5C%5Cf%28x%29%3Dx%5E%7B3%7D-3x%5E%7B2%7D%20%2B4x-2)
Answer:
y > -1/2 x + 4
Step-by-step explanation:
Equation of a line : (y-y1)/(y2-y1) = (x-x1)/(x2-x1)
(y-4)/(2-4)= (x-0)/(4-0)
(y-4)/-2 = x/4
(-y+4)/2 = x/4
-y+4 = 1/2 x
-y = 1/2 x - 4
y = -1/2 x + 4
the solutions of the inequality are the points above this line, so
y > -1/2 x + 4
Since y intercept if one, i automatically know the answer is y = 1/2x + 1. The second one