Chapter 12 Sequences and Series - Using Alternative Methods - Another Way to Solve Example 4 - Practice - Page 835: 5

See below.

Assuming the sequence has a limit $L$, the value that the sequence approaches as $n$ becomes large is: Then our equation is: $L=0.25L+300\\0.75L=300\\L=400$. The sequence approaches the limit $L=400$ as $n$ becomes large.