Given an iterative algorithm below which defines the $+1$ elements of vectors $$ and $$:

$(+1)=10()$

$(+1)=()+$

$()$

$500$

$(1)=10,(1)=0$

a$.$ Find the value of A and B on the $3$rd iteration.

b$.$ Find the value of A and B on the $1000$th iteration.

c$.$ What are the steady state values of A and B $($i$.$e$.,(),(),->\backslash$infty $)?$

d$.$ Create good plots of A and B as a function of iteration number.