For each sequence given below, find a closed formula an for the nth term of the sequence (assume the first terms are ao) by relating it to another sequence for which you already know the formula. (a) 4, 5, 7, 11, 19, 35, ... (b) 0, 3, 8, 15, 24, 35, ... (c) 6, 12, 20, 30, 42,... (d) 0, 2, 7, 15, 26, 40, 57, ... (Hint: These might be called "house" numbers, as in "house of cards")

Please solve.

3.) Given this truth table, find the unoptimized formula this corresponds to, along with the version which was optimized with a K-Map. A B C D O 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 0 1 1 1 1 0 0 0 1 0 0 1 1 0 1 0 1 0 1 1 1 1 0 0 1 1 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 0 0 1 0 0 0 1 0 0 0 Unoptimized Sum of Products equation 3a) 0 = Draw the K-map and simplify Optimized Sum of Products equation 3b) 0 =

Matlab code

1. we use a cubic equation in which the variables and coefficients all take on values in the set of integers from 0 through p - 1 and in which calculations are performed modulo p for a ------------------ over Zp. 2. A ----------- GF(2m) consists of 2m elements together with addition and multiplication operations that can be defined over polynomials.

ts) The phase plot for an ODE - f(N) is shown below. (a) Which of these could be a plat of solutions y vs z comresponding to this CDE? A. B. C. D. You can cilck the graphs above to enierge them. OA. A OB. B OC. C OD. D (D) One equilibrium solution af this ODE is y which is chogse and another equilbrium solution of this CDE is y - which is choase (C) For which of the following value(s) of the initial condtion y(0) does the solution g(z) converge as z 00? Select all that apply DA. 0) - 3 OB. 0) - 3.5 OC. p(0) - 2 OD. (0) - -1

Please make a k-map to simplify the given boolean equation (and list the final simplified expression)(((((Y AND (~Z)) OR ((~Y) AND Z)) OR (~Z)) AND (~(X OR Y))) OR (~(((Y AND (~Z)) OR ((~Y) AND Z)) OR (~Z))) AND (X OR Y))