Answer
Convergent to 0
Work Step by Step
We are given the sequence:
$a_{n+1}=4a_n(1-a_n)$
$a_0=0.5$
Compute the values for $a_n$ when n=0,1,2,3:
$a_0=0.5$
$a_1=4(0.5)(1-0.5)=1$
$a_2=4(1)(1-1)=0$
$a_3=4(0)(1-0)=0$
We notice that the sequence is convergent and its limit is 0.