We have sequence equation
.
In this case n is a natural number (1, 2, 3, ...).
So start inserting and computing value of
given that you know the value of n and a.
(first term)

Hope this helps.
I don't understand what you're asking, is there supposed to be a picture with the question?
First: the homogeneous solutions: the characteristic equation is4r^2 - 4r - 3 = 0which has roots r = 3/2, -1/2 hence the homogeneous solution isy = c1.exp(-x/2) + c2.exp(3x/2)
next you need the general form for the guess for yp and that isyp = A1cos(2x) + A2sin(2x)
Now substitute that into the equation and solve for A1, A2.
Hi, sadly I am
not sure. Do you maybe mind explaining what rooster or your lesson is? Comment to me and Ill be glad to help!