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given a recursive sequence : J(n)=b*A(n)  for b=0.5 , A(0)=70% , n is integer

wrote a procedure to find J(n), for example: find J(5)=?

i need help with this please .

i have a D.E. systems:

J_n=2A_n

S_n+1=J_n

A_n+1=S_n+0.5A_n

and initial conditions A₀=10, J₀=30, S₀=5

can i use rsolve to solve this or is there another ways to solve this systems

i tried to plot a differential equation with piecewise.

g3:=diff(y(t),t)=((800-y(t))*y(t)/*(100+y(t)))-E*h

ivs6:=[y(0)=100,y(0)=500,y(0)=1500]:

with(DETools):

DEplot(g3,y(t),t=0..10,ivs6);

how to find the equilibrium point of a differential equation y'(t)=(800-y(t)).y(t)/(100+y(t))