Suppose that the sequence x0, x1, is defined by x0 = 4, x1 = 0, and xk+2 = 3xk+1+4xk for k≥0. find a general formula for xk. be sure to include parentheses where necessary, e. g. to distinguish 1/(2k) from 1/2k

A general formula for the  sequence  is .

Step-by-step explanation:

Given a linear homogeneous recurrence of the form , with constant coefficients ,   and initial conditions ,   has a characteristic equation given by the formula , this equation has a degree 2 and has two roots and . If then is a solution of the recurrence relation, where and are the solution of the system

From the problem we know that and are the inicial conditions and and . In order to find the general formula for , first we find  its characteristic equation

⇔⇔⇔ ∨

Now we need to find   and   using the initial conditions  and , we need to solve the system of equations

you can add the two  equations and find the values and ,  so a general formula for is  .

for finding the midpoint of any given 2 pair of points simply add the respective x coordinates with other x coordinate and the y coordinate with other y coordinate and divide them by 2

in your question it will be :

(3+1)/2 for the x coordinate of mid point i.e 2

[8+(-4)]/2 for the y coordinate of midpoint i.e 2

so coordinates of mid point of points (3,8) and (1,-4) will be (2,2)

step-by-step explanation:

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