# Créé par shemon, le 26/01/2023 en Python 3.7
# section 7 : suites récurrentes
print("question 1. cas arigeo")
from math import*

print("quest a)")
def U(n):
    u=5
    for k in range(n):
        u=2*u-3
    return(u)

print("quest b)")
for k in range(6):
    print("U=",U(20+k),"n=",20+k)

print("quest c)")
def Uag(a,q,r,n):
    u=a
    for k in range(n):
        u=q*u+r
    return(u)

def arigeo(a,q,r,n):
    x=r/(1-q)
    u=(a-x)*q**n+x
    return(u)
print("faites des tests")
print("quest d)")
print("test explicite", "u15=",arigeo(-1,1.32,1,15))
print("test récurrente", "u15=",Uag(-1,1.32,1,15))