Answer:
60
Step-by-step explanation:
For a recurrence relation
[tex]u_{n+1}[/tex] = a[tex]u_{n}[/tex] + b
If - 1 < a < 1 then a limit exists and is calculated as
L = [tex]\frac{b}{1-a}[/tex]
Given
[tex]u_{n+1}[/tex] = 0.75[tex]u_{n}[/tex] + 15
with - 1 < 0.75 < 1
a = 0.75 and b = 15, thus
L = [tex]\frac{15}{1-0.75}[/tex] = [tex]\frac{15}{0.25}[/tex] = 60
