(1 point) We will find the solution to the following lhcc recurrence: On = 30n-1 + 4092 for n > 2 with initial conditions ao = 3,01 = 8. The first step in any problem like this is to find the characteristic equation by trying a solution of the "geometric" format an = guna (We assume also r = 0). In this case we get: pode = 3-1 + 47.-2. Since we are assuming ? * O we can divide by the smallest power of r, i.e., you-2 to get the characteristic equation: 72 = 3r + 4. (Notice since our lhcc recurrence was degree 2, the characteristic equation is degree 2.) Find the two roots of the characteristic equation m and my. When entering your answers use ri sm P1 = 2 = Since the roots are distinct, the general theory (Theorem 1 in section 5.2 of Rosen) tells us that the general solution to our lhcc recurrence looks like: dr = 01 (ru)* + 02 (12) for suitable constants 01, 02 To find the values of these constants we have to use the initial conditions ao = 3,01 = 8. These yield by using n=0 and n=1 in the formula above: 3 = 01 (1) + 02 (2) and 8 = 01 (ru)' + 02 (12) By plugging in your previously found numerical values for ri and my and doing some algebra, find 01, 02: [Be careful to note that (-x)" + - (**) when n is even, for example (-3)2 + - (32).] 01 = 02 = Note the final solution of the recurrence is: on = 01 (ru)" + 02 (2) where the numbers 7,0; have been found by your work. This gives an explicit numerical formula in terms of n for the On