How do I write a code for a linear system in the form a(n+1) = c*a(n) + b

How do I write a matlab code to solve a linear dynamical system of equations in the general form of a(n+1) = c*a(n) + b with an initial value a_0 and the steps range from 1 to N

[Walter Roberson]

This is not a linear system.

Suppose b=0 and a0=1. Then a1=c*1, and a2=c*c and a3=c*c^2 and so on, so the general form would be a(n) = c^n. This is not linear.

[Francesca Esquivel]

Ok, then how would I write a code that would solve the system i have written?

[Walter Roberson]

a_0*c^n-b/(c-1)+b/(c-1)*c^n

is the general solution

Answer 1

[KSSV]

N = 100 ; 
a0 = rand ; % initial a 
b = rand ; c = rand ; 
a = zeros(N,1) ; 
a(1) = a0 ; 
for n = 2:N
    a(n) = c*a(n-1)+b ; 
end

[Carlyn Thomsen]

If I wanted to plot the results for the values of a(n), with an a(n) vs n graph, what would be the code for that?

[Walter Roberson]

plot(a)