Chapter 12 Sequences and Series - Using Alternative Methods - Another Way to Solve Example 4 - Practice - Page 835: 2

See below.

Assuming the sequence has a limit $L$, the value that the sequence approaches as $n$ becomes large is: Then our equation is: $L=0.38L+512\\0.62L=512\\L\approx825.8$. The sequence approaches the limit $L\approx825.8$ as $n$ becomes large.